# Differential equations questions and answers

Recent questions in Differential Equations

### I have to solve following system of equations:${x}^{″}=-x-z+{e}^{-t},{z}^{\prime }=-2x-2z+3{e}^{-t}$I would like to have formula for x' in order to find fundamental matrix and so on. So from above quations I obtain ${z}^{\prime }-2{x}^{″}={e}^{-t}$, integrate sides and have $2{x}^{\prime }=z+{e}^{-t}$So I have system of two first-order differential equation$2{x}^{\prime }=z+{e}^{-t},{z}^{\prime }=-2x-2z+3{e}^{-t}$Is it correct?

Bacille John Purca 2022-05-18
Bacille John Purca 2022-05-18
Bacille John Purca 2022-05-18