Differential equations MOC

Homogenous linear ODE with constant coëfficients

In the majority of cases solving a homogenous linear ODE with constant coëfficients

equates to solving the characteristic equation

where for any such a solution is given by . In the cases where there are repeated roots, a method such as reduction of order must be used to find a complete basis of solutions.

Second order

In the second order case

the characteristic polynomial is

and a solution is given by

If (repeated roots), then an additional linearly independent solution is

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