- #1

vikkivi

- 4

- 0

## Homework Statement

Solve the inhomogeneous differential equation dX/dt=AX+B in terms of the solutions to the homogeneous equation dX/dt=AX.

## Homework Equations

A is an nxn real or complex matrix and X(t) is an n-dimensional vector-valued function.

If v is an eigenvector for A with eigenvalue a, then X=v*e

^{a*t}is a particular solution to the differential equation dX/dt=AX.

And the general solution of the homogenous eqn is X=P

^{-1}*Xtilda.

## The Attempt at a Solution

So, the general solution of the inhomogeneous equation should be a particular solution of the inhomogenous equations + the general solution of the homogeneous equation. We know the general part, but I am lost on how to find the particular solution for an inhomogeneous equation. Any help would be apprecaited!

Last edited: