# Questions tagged [differential-equations]

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

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### Using NDSolve and PieceWise for boundary conditions for coupled PDEs

I've decided to try and use PieceWise in my boundary conditions for my 4 coupled PDEs, but it doesn't seem to work out nicely. I'm receiving the error: NDSolve::overdet: There are fewer dependent ...
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### Two different plots of the same solution from NDSolve!

I used NDSolve to solve the system ...
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### Differential equation solution

DSolve[y''[x] + (a - (b*x^2 - c)*x^2)*y[x] == 0, y[x], x] I couldn't solve this equation, please help
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### Confluent Heun function

Does this function (confluent Heun function) exist in Mathematica? I try to solve the following equation, ...
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### Hopf bifurcation for competitive system

I am attempting to visually investigate a Hopf bifurcation in the xz plane in a competitive system but have no idea how to input some of these values so I may adjust some of the parameters as ...
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### Solving and plotting derivative included function

Please suggest a method that I can use to solve (for y(x) and y'(x)) and plot the derivative related given function. Note: L may be vary): ...
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### Can this PDE be solved through DSolve?

I was trying to solve the linear advection pde, using DSolve. I was able to do it using NDSolve, but I was curious to see if Mathematica was able to give the well-...
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### Manipulate NDSolve

Can anyone help me? This is my code: f[x_ ] = x Exp[I z]] (Cos[z]] BesselJ[l, a *x] - BesselY[l, a *x] Sin[z]) u=0.1 v=6 on the other hand hand: ...
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### Plot an Integral of NDSolve solution

I have a problem with plotting the integral of an NDSolve solution. I have attached the code for a simple 2nd order linear ODE to be solved by NDSolve and then to be integrated by NIntegrate. I ...
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### I there any way to DSolve an equation by an estimated method?

I am trying to DSolve this differential equation for A[r] ...
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### Need help solving ODE with ParametricNDSolveValue solver

I am trying to apply @bbgodfrey method for finding the right initial guess for the following problem but I get an error message and I don't understand where it comes from. I would also like to ...
51 views

### Calculating with deformed Heat equation?

How can I implement the following equation and start computing numerically? The first partial derivative can take fractional numbers.
148 views

### The NDSolvevalue of MMA can not be used to solve the finite element problems according to the stress boundary conditions

The NDSolvevalue of MMA can well solve the finite element problems according to the displacement boundary conditions ...
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### I can't draw the Plot [closed]

I'm running the below code, but it draws an empty graph, and I don't know how to fix it. ...
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### NDSolve error when integrating two second order coupled ODEs

I want to plot a solution for a system of two second order coupled ODEs: ...
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### Adjusting PrecisionGoal and AccuracyGoal when solving my equation using NDSolve?

Thanks for paying attention to my question and modifying my terrible formatting[facepalm], now I think I've found the answer. The point is the selection ...
45 views

### Error message when trying to solve 2 coupled PDEs using NDSolve

I'm currently facing a problem when trying to solve 2 coupled PDEs. I get the warning messages: NDSolve::fembdcc: Cross-coupling of dependent variables in DirichletCondition[IPF==IPB/10,z==5.] is not ...
63 views

### Plotting a two parameter function evaluated at a specific point

I am trying to solve the following problem: given the differential equation $$\frac{d^2y}{dx^2}+\bigg(a+b\frac{2}{\pi}\tan^{-1}x\bigg)y=0$$ subjected to two different initial condition we get two ...
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### DSolve function is not working for Hypergeometric Function

I am trying to get the solution of second order differential equation, but it is not working. Any idea about it will help me a lot. ...
817 views

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### Solving Piecewise Differential Equation using NDSolve (coupling at BC)

I am having some issues in dealing with a system of differential equations. I would like to solve a 1D diffusive heat equation across several regions with different material properties. I now have a ...
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### Fit a three-pulse sequence

I am wondering how to properly fit the three-pulse sequence shown below. I have tried a method which is fitting the three pulses with three polynominal functions seperately and then finding the x-...