Mathematica Tutorial

Inhomogeneous Linear Second-Order Equations

If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem.

This solves an inhomogeneous linear second-order ODE. The solution is composed of two parts: the first part is the general solution to the homogeneous equation, and the second part is a particular solution to the inhomogeneous equation.

In[1]:=

Out[1]=

This solves the homogeneous equation, which is an Euler equation.

In[2]:=

Out[2]=

Different particular solutions can be obtained by varying the constants C[1] and C[2] in the solution.