Differential equations MOC

Solving non-homogenous second order ODEs

For any second-order ODE

it is clear that the difference of any two solutions solves the related homogenous ODE. Namely, given and , it is clear that

It follows that given the general solution to the related homogenous ODE , called the complimentary solution, and any one particular solution to the full ODE , then

since

Finding a particular solution

In practice, a variety of methods may be used to find a particular solution once has been found

• Method of undetermined coëfficients (uses an Ansatz)
• Method of annihilation
• Method of variation of parameters (similar to Reduction of order (homogenous second-order differential equation))

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