Matias Aguirre

2022-07-28

Show that the function defined in column I is a solution ofthe corresponding differential equation in Column II in everyinterval a1. $f\left(x\right)=x+3{e}^{-x}$
2. dy/dx+y=x+1

kamphundg4

Expert

Given
$y=x+3{e}^{-x}$
$dy/dx=1-3{e}^{-x}$
Now for the second equation
dy/dx + y =
$\left(1-3{e}^{-x}\right)+\left(x+3{e}^{-x}\right)=$
= 1 + x

Joanna Mueller

Expert

$\frac{dy}{dx}=1-3{e}^{-x}$
$\frac{dy}{dx}+y=1-3{e}^{-x}+x+3{e}^{-x}=x+1$
so $f\left(x\right)=x+3{e}^{-x}$ is the solution of dy/dx + y =x=1

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