# Questions tagged [differential-equations]

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

3,826 questions
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### How to Solve this ODE with Mixed Boundary condition

I have an ODE equation which is sort of y''[x] + 2 y'[x]/x + .0001 (y[x])^3 ==0 subject to the boundary conditions ...
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### Starting NDSolve from intermediate time step?

I always wondered if I could start NDSolve from an intermediate time step. What I mean is, in the code sample below, if I were to run my solution from ...
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### DSolve cannot solve for certain branches of the solution

Update - This has been fixed in 10.0.0 Could somebody please tell me, why I am always getting an error message when trying to run the following code: ...
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### How can I solve a difference-differential equation?

How do I ask Mathematica to try to solve a recursive relation that defines a sequence of functions? For example, suppose I know that $g_n(x) = g_{n-1}'(x)$ for $n > 0$ and that $g_0(x) = e^{2x}$. ...
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### Solution Curves and Order of Evaluation Question

I'm new to Mathematica, so I thought I'd try to exercise some solution curves. Consider a simple first order ODE: $y'(x)=\cos(x)$. We know the solution will be of the form $y = \sin(x)+c$ I ...
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### How to apply restrictions to the “integrated” variable, when using NDSolve?

I have to integrate an energy along a path. I know the energy at the "beginning" of the path (energy[0]), and I can determine the energy change (gain and loss) ...
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### MaxSteps and Computing time issue for Solving Differential equation in Mathematica

When we solve differential equation numerically using NDSolve then sometimes we get error like NDSolve::mxst: Maximum steps reached According to Mathematica docs ...