# Tagged Questions

Questions on the symbolic (DSolve, DifferentialRoot) and numerical (NDSolve) solutions of differential equations in Mathematica.

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### How to tell NDSolve about known relations of the exact solution

The solution to this system of differential equations: ...
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### Customizing display of partial differential equations

I am manipulating partial differential equations symbolically, and would like to get the easily readable form $\rho \frac{\partial v}{\partial t}$, leaving variables implicit. Based on suggestions ...
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The original system of equations reads: $\begin{cases} f'(r) + f(r) \left(a(r) - \frac{1}{r}\right) = 0,\\ f^2(r) + a'(r) + \frac{a(r)}{r} - 1 = 0\,, \end{cases}$ with boundary conditions $f(0) = 0\,... 0answers 104 views ### DSolve solves PDE only without boundary condition, but fails otherwise I'm trying to solve for Te[w, Pprobe, t] in a partial differential equation. What's surprising is that it manages to solve it when I don't put in any initial ... 0answers 122 views ### EquationTrekker-like behavior for state space? EquationTrekker is great for phase space plots, however I want to plot the results of $$\phi '(t)=-b \sin (\phi (t))+g \sin (\Phi (t)-\phi (t))+1\\\Phi '(t)=g y \... 1answer 312 views ### Issue in ParallelTable after evaluating another function using NDSolve and FindRoot. What is wrong with this inverse? I am trying to find the inverse of a function which is defined through NDSolve and NIntegrate. The question is pretty similar ... 1answer 111 views ### Already solved DE, now I need to rearrange and plot I have solved for z(w,x,y) in a differential equation:$$ 3\frac{\partial z}{\partial y} = 2(z-1) + (1-wy^2 )x $$And I obtained the general solution: z = f(w,x,y) Now putting in x=0, we have ... 1answer 1k views ### How to solve fluid flow problem based on Navier-Stokes equations? Does anyone know or can provide any examples how fluid flow problem can be formulated and solved in Wolfram Language? Simplest cases of 1D or 2D flows based on Navier-Stokes equations or even their ... 2answers 92 views ### Solve simple differential equation - Error? I get the error "The function Te appears with no arguments." when running this code. I'm not sure why. Is it because of the Abs[\Gamma] ? ... 3answers 4k views ### how to solve ODE with boundary at infinity y''[x]-x y[x]==0 y[0]==AiryAi[0], y[infinity]==0 the analytic solution to this ODE is the Airy function y[x]=AiryAi[x] if I ... 2answers 782 views ### Plotting a solution of the Allee Effect I am doing a project on the Allee Effect. I am able to successfully create a stability analysis. That is, I can find the relevant equilibrium points (y_e = 0,\ y_e = \alpha and y_e=k) and draw ... 1answer 200 views ### DSolve problem with system of linear ODEs I encounter a rather strange problem in Mathematica when trying to solve the following system of linear differential equations: ... 0answers 269 views ### Problem with NDSolve in Mathematica 9 / 10 I'm having trouble by solving the following differential equation in Mathematica 9 and 10, where the code works fine in version 7: ... 1answer 329 views ### Using spherical derivatives with NDSolve I am trying to plot the path of an object around a centre of mass. Obviously this needs spherical coordinates. The problem I encounter is with the derivatives. The Derivatives in spherical coordinates ... 2answers 154 views ### Automatically detect largest interval over which NDSolve can find a solution Question: Consider the following numerical resolution: NDSolve[eqn, {x1[t], x2[t], y[t]}, {t, tmin, tmax} where eqn, ... 1answer 162 views ### Is it possible to obtain explicit symbolic solutions to such linear ordinary differential equations? The ordinary differential equations to solve have symbolic parameters k_1,k_2,k_3,k_4,k_5,k_6 \in \mathbb{R}.$$ \left\{ \begin{array}{l} {y_1}'(t)=-{k_1} {y_1}(t)-{k_2} {y_1}(t),\\ {y_2}'(t)={k_2} {... 1answer 2k views ### Solving a nonlinear PDE with Mathematica10 FEM Solver I am trying to solve a system of coupled nonlinear PDEs in a rectangular region with the new FEM solver in Mathematica 10. However, I come across an error stating NDSolveValue::femnonlinear: ... 1answer 253 views ### When plotting vector fields what is the difference between the following? I am a new Mathematica user, and I have run into a question. What is the difference between the output of the commands: ... 2answers 445 views ### Problem when defining function through NIntegrate and NDSolve and Interpolation - Bug? More than a single question, I have some doubts about the output of certain functions when defined through the result of other calculations. I am an active user of Mathematica, but maybe I haven't ... 1answer 593 views ### Solve ODE$d^2u/dx^2 + u/A = 0$How can I solve following ODE with Mathematical: $$d^2u/dx^2 + u/A = 0 \quad (\text{or } \ C),$$ with the conditions: $$\left.\frac{d^2u}{dx^2}\right|_{x=0} = 0,$$ $$u(x=0) = B$$ and $$\left.\... 1answer 198 views ### WhenEvent “StopIntegration” problem The first example on the WhenEvent help page is ... 0answers 190 views ### NDSolve with Table and Boundary Conditions I am trying to implement a 1D model of coupled field equations where I split up space into pieces to get a system of coupled ODEs which I call Eeqns and Ieqns. The problem I can't figure out is how to ... 2answers 247 views ### How do I plot the differential of this function? Suppose I have this function:$$z(x,y) = \left| \frac{ \frac{1}{3x +iy} -2x}{iy + \frac{1}{x}} \right| $$I want the contour plot of \frac{\partial z}{\partial x} with axes (x,y). Tried this ... 2answers 207 views ### How do get an output table or a plot of individual variables from NDSolve output I have the following equations and settings: ... 0answers 51 views ### How to fit data with numerical solution of system of parametric ODE? [duplicate] I need to find the parameters (k1,k2,k3,k4,k1r,k2r,k3r,k4r) that fit my data (list of [Intensity, time]) using the function <... 3answers 4k views ### Numerically solving Helmholtz equation in 2D for arbitrary shapes I would like to solve the Helmholtz equation with dirichlet boundary conditions in 2 dimensions for an arbitrary shape. (for a qualitative comparison of the eigenstates to periodic orbits in the ... 0answers 41 views ### How can Mathematica solve 7 equations and want to find 7 variables [duplicate] I have 7 equations as below * e1 := (1 - a) p Subscript[A, 0] Subscript[s, K ] ! *SubsuperscriptBox[(s), (L), (-a)] = (1 - b) Subscript[B, 0] (1 - Subscript[s, K]) (1 - Subscript[s, L])^-b; ... 1answer 270 views ### How to get solution from DSolve How to get the solution from DSolve in such way that there is no need to copy the result. When for example solving: ... 2answers 282 views ### NDSolve fails to solve vector-valued function x'[t] == a . x[t] + u . b I get no solution when I run the following command: ... 3answers 921 views ### Can NDSolve handle discountinuos data? It is possible to numerically solve a differential equation if not-smooth data are involved? For example the following instruction return the error NDSolve::bvdisc: ... 1answer 319 views ### Partial Differential Equation in Parallel is there any native way to implement multi-core parallel solving of PDE in Wolfram Mathematica? WM 10 now supports Finite Elements Method, but it is actually useless without parallelization. Usually ... 1answer 186 views ### NDSolve: EventAction list specification using Table fails I have an NDSolve problem that needs a list of a large number of events that are generated programmatically. Here is a simple example that demonstrates the problem on Mathematica 7 and 8 (the versions ... 0answers 270 views ### NDSolve PDE, not enough boundary condition? The PDE that I want to solve is:$$ \frac{\partial f}{\partial t} + \frac{1}{m} \left( p_x \frac{\partial f}{\partial x} + p_y \frac{\partial f}{\partial y} + p_z \frac{\partial f}{\partial z} \right) ... 1answer 127 views ### 1/0 encountered when solving an ODE What can cause this error to show up? Clear[lambda, a, b, x, y]; ode = lambda y[x] + a b y'[x] + a (-1 + b x) y''[x] + y''''[x] == 0; DSolve[ode, y[x], x] ... 0answers 71 views ### Error solving third order ODE in version 10. No error in V9. DSolveDSolveKovacicDump This is an ode which is solved with no error in V9, but gives a very strange error in V10. Is this a regression bug? On version 9, the ode is solved with no error ... 0answers 207 views ### Solving PDEs with complicated boundary conditions [duplicate] The system I'm trying to solve is $$\nabla^2 C_{(r,\theta)} =0$$ $$C_{(\infty,\theta)}=C_0$$ $$[ \frac{\partial C_{(r,\theta)}}{\partial r} \cos(\theta)+\frac{1}{r}\frac{\partial C_{(r,\theta)}}{\... 3answers 2k views ### Symbolic solution(s) to generalized Heat equation Symbolic solution(s) to Heat equation? or more generally,(eventually) Green functions to known PDEs I am interested in variations of the heat equation: or more generally or even more generally ... 0answers 124 views ### DSolve breaks when the ordering of independent variables aren't proper? Bug introduced in 5.2 or earlier and persisting through 10.4.1. I encountered this when trying to solve this problem with DSolve: ... 1answer 254 views ### Use NDSolve to solve a PDE I have the following PDE (a master equation, and P is probability density, 0\le x\le1 and 0\le y\le1):$$ \partial_t P(x,y,t)=x\partial_xP(x,y,t)+(1-y)\partial_yP(x,y,t)+2P(x,y,t) $$The ... 4answers 677 views ### Should DSolve always return solution with constant of integration? Bug introduced in 10.0.0 and fixed in 10.0.2 Clear[y,x]; DSolve[D[y[x], x] - y[x]^2 + y[x]*Sin[x] - Cos[x] == 0, y[x], x, GeneratedParameters -> C] or ... 1answer 160 views ### Factoring a differential equation into an operator product Following the fundamental theorem of algebra, I can (as stated here in Sec. 1.1.4) factor an nth-order linear ordinary differential equation$$ a_n \frac{d^n x}{dt^n} + a_{n-1} \frac{d^{n-1} x}{dt^{... 0answers 414 views ### Speeding up NDSolve for system of differential equations I am wondering if there is a way to speed up this function that solves a system of ordinary differential equations with NDSolve? Thus far I've tried specifying a few different methods such as LSODA, ... 0answers 143 views ### Apply IC and BCs on Second - Order Linear PDE I am now trying to solve second - order linear partial differential equation in that interested eq. has been separated into variables to simplify the procedure for Mathematica. Here is my equation; ... 1answer 213 views ### Why DSolve giving Inconsistent or redundant transcendental equation on this problem Kamke's differential equation #574 has a solution, but Mathematica generates an error message as it tries to solve it. It still gives the solution. My question is: What could have caused Mathematica ... 1answer 229 views ### How do I subtract two contours? Suppose I have this contour described by the equation the root$z$of this equation $$\frac{1}{x^2 + y^2} + \frac{1}{xz} = 2y$$ Now suppose the equation is tweaked slightly, with an addition of$w$... 2answers 301 views ### Poincaré Section I have encountered somewhat the same problem as here. But with the equations,$x'(t) = p(t), p'(t) = - x(t) - y(t), y'(t) = q(t), q'(t) = - y(t) - x(t)$My code is, ... 0answers 161 views ### Optimizing a functional using variational calculus Here I am, trying to get the trajectory$(x(t),y(t))$that will minimize the following Lagrangian (i.e. the integrand of the functional) between$(-1,-1)$and$(-1,y_{eff})$where$x_{eff}$is defined ... 2answers 361 views ### Problem with Poincare section these are equations for some double oscillators:$x'(t)=p, p'(t)=-x-3y, y'(t)=q, q'(t)=-y-3x$I would like to plot the Poincare section for collection of$(y,q)$when$x=0$and$x'(t)>0$(or for$...
Suppose we have this differential equation: $$x^2 + y^2 + z^2 = \frac{\frac{\partial y}{\partial x}}{x+y+z}$$ I want to find $\frac{\partial y}{\partial x}$ at x=1,y=1,z=1. I tried this code but ...
Suppose we have this equation: $$2 - x g(z) f \left(x, \frac{\partial y}{\partial x}\right) = 3y$$ using initial condition $y = 2$ where $g = \left| \frac{3}{2-iz} \right|$ and \$f = \frac{2x}{1-...