# Questions tagged [differential-equations]

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

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### How to check numerical values on a plot? [closed]

Suppose we have the model: ...
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### How to numerically solve this system?

Our system: \begin{align} \dot S &= \mu -\beta_1 S I_2 -\beta_2 S J-\beta_3 S A - \nu S\\[2ex] \dot {I_1} &= p \beta_1 S I_1 +q \beta_2 S J +r \beta_3 S A + \xi_1 J- b_1 I_1 \\[2ex] \dot{...
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### Error complex function ERFI(X): looking for alternative function representations?

I have some analytical results from a physics problem, where the Mathematica gives the results in terms of complex error function. I would like to explore another function representation using ...
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### How to re write the solution to this pde [closed]

I have this equation solved: ...
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### Dog-Owner problem(pursuit curve)

A dog in the coordinate system starts from the origin along the x-axis with vk=1m/s speed. The owner starts from the (0,1) point running towards the direction of the dog with vg=2m/s speed.Show the ...
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### Using NDSolve with Interpolated Functions

I'm trying to run code designed to solve for a particle's spin given its velocity. The particle is in a rotating fluid with (in this case) parallel external electric & magnetic fields. The code, ...
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### Lotka-Volterra in mathematica

I have to solve the next problem: We know that a=b=c=d=1 and x0=2,y0=3,q=0.2,On the t=[0,20] interval there is no fishing but on the t=[20,40] interval there is.Show the adequate trajectory(the first ...
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I'd like to plot the Poincaré section based on the problem from here: see exercise 8.1 Given that the standard logistic equation with harvesting function is $$\dfrac{dx}{dt} = ax(1 - x) - h (1 + \sin{... 1answer 66 views ### Solving Second Order Differential Equation with Discrete Time Data Given the Second Order Differential Equation:$$ m\ddot{x}+c\dot{x}+kx = \mathrm{F}_{external}^{} $$where  m, c, k  are constants and \mathrm{F}_{external}^{} is buffer of external force taken ... 2answers 63 views ### Getting ODE solution in forms other than exponential or as a pure function I'm new to Mathematica and trying to solve some ODE's through it. But, whenever I try solving these ODE's I get pure functions as solutions with exponents only. Here's a pic for example. Now, if I do ... 1answer 71 views ### optimization with multiple parameters and differential equations There might be some relevant questions and answers, but I couldn't complete my code by myself just by reading them. Sorry that I am very new to Mathematica and my question could be a bit rough and not ... 1answer 108 views ### Finite difference method for solving coupled differential equations I am trying to solve the following coupled differential equations: \dot{c}_{1}(t)=-\int_0^t \alpha_{1}(t,s)c_{1}(s)+\beta_{1}(t,s)c_{2}(s)\,ds-\frac{i}{\hbar}\lambda c_2(t)e^{+i(\omega_1-\omega_2) t}... 0answers 102 views ### How do i solve two coupled nonlinear PDEs through Mathematica? these are two relativistic fluid governing equations, ∂_t (γe)+∂_x(γev)=0 γ∂_t(γv)+∂_x[(γv)^2/2]=-(C/(1+C))*∂_x[log(e)] where γ=1/sqrt(1-v^2) is Lorentz factor, <... 1answer 54 views ### DSolve Second Order Differential Equation with One Boundary Condition [closed] So I set up my singular perturbation problem after change of variables for equation and boundary condition. But when using DSolve for the analytical solution, there's always a 1/2 in front of it. Can ... 2answers 178 views ### NDSOLVE mathematica fluid mechanics i have made mathematica code for equation 16 . . using it 1st time and facing a lot of errors . . can some guide about the problem. . guidance according to FLUID MECHANICS field would be great ... 1answer 34 views ### DSolve subject to [closed] I want to compute two differential equations with subject to conditions. My solution: ... 0answers 92 views ### I want MathLie setup for mathematica [duplicate] I tried to find Math lie in Mathematica but I didn't find setup. Can anyone share Math lie setup for Mathematica? 0answers 91 views ### NDSolve::ndsz error: singularity or stiff system suspected | Coupled ODEs [closed] I am new to Mathematica. Trying to solve the below coupled-ODEs (eqnA, eqnB, eqnC). However, getting error NDSolve::ndsz: At x == 0.8849324488967629, step size is effectively zero; singularity or ... 1answer 152 views ### Calculating the 3D Vector field of a permanent magnet with FEM trying to calculate the magnetic field of a permanent magnet using the finite element method I struggle setting up the equation system properly. In the end I want to be able to calculate the magnetic ... 2answers 154 views ### Why the difference in fundamental solutions? Finding a fundamental solution of a linear differential operator f''-c^2f, I try in 12.3.1 on Windows 10 DSolve[f''[x] - c^2*f[x] == DiracDelta[x - y], f[x], x] ... 0answers 43 views ### solve pde with moving top boundary I am trying to solve this pde (1D diffusion with source term) with a top boundary that moves over time noted as L0[t]. The NDsolve works when L0=constant, but here the top boundary changes in height ... 1answer 115 views ### Simple hybrid ODE cannot be solved symbolically Mathematica solves the following very simple hybrid ODE without any problem: DSolve[{x'[t] == 1, x == 0, WhenEvent[x[t] == 2, x[t] -> 0]}, x[t], {t, 0, 5}] ... 0answers 50 views ### Solution to differential equation only starts at random times (numerical error?) I am solving a set of differential equations with an oscillatory forcing (square wave). Instead of the solution starting to oscillate immediately it stays still until some time. That varies with small ... 1answer 84 views ### The heat equation on the intervall [0,1] with Robin Boundary I have the heat equation on the invervall [0,1], therefore I define heqn = D[u[x, t], t] == D[u[x, t], {x, 2}]; and I define my initial data which can be boring, ... 2answers 84 views ### How to realize NDSolve by NSolve with the implicit constraint equations? Daniel post the amazing code to realize numerical integrators, I think it is useful to the kind of one-step explicit equation like x[k+1]-x[k]== constant_number. In ... 0answers 36 views ### Fitting coupled ODEs on data I'm learning how to fit a system of two ODEs to data. The dataset is in the form dataset=Transpose[{time,datax,datay}] {{0.,0.,0.},{0.1,0.283791,0.0949328},...} ... 1answer 53 views ### How to realize NDSolve by Solve? I want realize the NDSolve by Solve,so I read some numerical integration resource. In common setting, ODEs can be solve by Euler ... 0answers 32 views ### Converting 1D map into first order differential equation for bifurcation diagram code I have existing code to plot bifurcation diagram for coupled first order differential equations. It seems to work for coupled differential equations. To test the code further, I use the simplest ... 1answer 60 views ### Plot When y axis data very small I use NDSolve solve the motion equation of a dynamic system. and When I plot the energy of the dynamic system, I find the y axis data is very small, I have take ... 1answer 51 views ### Ito process with white noise I would like to solve following system of SDEs, dx_i[t] = f[x_i[t]]*dt + dw_i[t] where d denotes ... 0answers 41 views ### Help!!! DSolve is coming out weirdly [closed] The equation I am entering is 𝑥2𝑦′′ +𝑥𝑦′ +𝑦=4ln(𝑥) and it looks like DSolve[x^2 y''[x] + xy'[x] + y[x] == Exp[4 Log (x)], y[x], x] , it comes out as ... 0answers 31 views ### Trouble with bifurcation of differential equation The code for bifurcation is written in such a way that it will allow plot bifurcation for any number of differential equation. Thus I am trying to avoid maps and iterations. Unfortunately it does ... 2answers 144 views ### Differential Equation in Complex Plane I asked this question 8 years ago, but the answer of @Jens was not satisfactory and it didn't reproduce the plot exactly. I'm wondering if new versions of Mathematica can handle it. 1answer 70 views ### Translating the \frac{u_x}{x}+\frac{u_y}{y}+\frac{u_z}{z}=\frac{u}{1-u}\quad u(\sqrt{y^2+z^2},y,z)=g(y) PDE into Mathematica notation? This may be silly, but I am trying to find solutions to the following differential equation:$$\frac{u_x}{x}+\frac{u_y}{y}+\frac{u_z}{z}=\frac{u}{1-u}\hspace{2cm} u(\sqrt{y^2+z^2},y,z)=g(y)$$On ... 1answer 114 views ### How to substitute a random function into a solution of a differential equation? I would like to solve a differential equation including a source term. The source term is a random variable and I model this by creating a list of RandomReal and ... 2answers 59 views ### Unable to plot a solution of NDSolve whilst being able to evaluate it I want to define a function f_c(x,y) as the solution of the PDE \Delta f_c(x,y) = g_c(x,y), where g_c is a given function depending on a constant c. I tried the following: ... 2answers 263 views ### How to solve this PDE I had a try at numerically solving the heat equation with a source term:$$ \frac{{\partial x}}{{\partial t}} = D\frac{{{\partial ^2}x}}{{\partial {z^2}}} + c $$... 2answers 81 views ### 3D plot of the spatial path of velocity/space stochastic differential equations I define the following 6 dimensional stochastic (Ito) process- in velocity v/position x. I can plot x1 as a function of t- see script below which has been corrected by Daniel. My goal is however to ... 0answers 50 views ### Solving a 1D diffusion equation [duplicate] I am new to Mathematica and I'm trying to find the analytical solution to the diffusion of excess pore pressure in a porous media using this equation:$$ \frac{\partial P}{\partial t} - \alpha \nabla^...
After solving an ODE with 'Solve' function, I'm getting a result as Now I know that the coefficients $c_1, c_2$ have to be zero when I impose further restrictions on the solution, so after obtaining ...