# Questions tagged [differential-equations]

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

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### Solving a Modified Biharmonic Equation on a Square

I am seeking to solve the differential equation \left[\partial_{\overline{x}}^{4}+2\left(1+\delta\right)\partial_{\overline{x}}^{2}\partial_{\overline{y}}^{2}+\partial_{\overline{y}}^{...
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### DSolve for System of Non-Homogeneous Differential Equation

Solve: x' = Ax + b Given: A = {{1, 2}, {3, 4}}; b = {{e^{t}},{2}}; This will solve if b == 0 DSolve[{x1'[t], x2'[t]} == a.{x1[t], x2[t]}, {x1[t], x2[t]}, t] But if ...
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### Solve a ODE with specific conditions

I am trying to find (some) functions h(x,t) such that A h(b,t)+B h_x(b,t)=g(t), where A,B,b are constants and g(t) is a given function of time (h_x is the partial derivative w.r.t. the first component ...
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### How can I plot 3-D system

If I have three equations nonlinear. I need to see the behavior around (0,0). How do I plot the three-dimensional system? Thank you in advance. I try to use this code ...
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### Turn vector equation into matrix multiplication

I have physical equations of motion that describe the dependence of one vector field on the components of another vector field. Without getting too much into detail, my differential equations involve ...
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### Geometrically nonlinear beam deflection

Edit only for those interested in large deflections of beams I discovered a mistake in the equations of the original question (below): in the normal force (compression/traction) ...
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### Why does NDSolve not give consistent results?

This is my code: ...
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### Newmark method to plot the displacement V/s time and phase plot of a plate

I am unable to plot the velocity V/s displacement plot (phase plot) of plate subjected to a dynamic load. I have generated the displacement V/s time plot, but the curve is not smooth. Also, my code ...
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### How to increase the speed of NDsolve when using WhenEvent

I am trying to solve a set of ODE's with switching. I implemented using WhenEvents. ...
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### Nonlinear dispersal equation modeling insect aggregation

I'm a newbie with Mathematica, I know it's a basic answer, but I can't solve the problem on my own. I have the following equation reflecting insect aggregation at low population densities (taken from ...