- #1

karush

Gold Member

MHB

- 3,269

- 5

$\tiny [9.1.98]$ solve

123

$\begin{array}{rl}

e^{5x}\,\frac{dy}{dx} + 5e^{5x}y

&= e^{4x} \\

\dfrac{d}{dx}\left( e^{5x}y\right)

&=e^{4x} \\

e^{5x}y&= \int{ e^{4x}dx} \\

e^{5x}y

&= \frac{1}{4}e^{4x} + C \\

y &= \frac{1}{4}\,{e}^{-x} + C\,{e}^{-5\,x}

\end{array}$

just reviewing some problems before Sept classes start up

I think this ok not sure how to check it with W|A

possible typos

Mahalo

https://dl.orangedox.com/wr9JnddSXWGHrASWF2

123

$\begin{array}{rl}

e^{5x}\,\frac{dy}{dx} + 5e^{5x}y

&= e^{4x} \\

\dfrac{d}{dx}\left( e^{5x}y\right)

&=e^{4x} \\

e^{5x}y&= \int{ e^{4x}dx} \\

e^{5x}y

&= \frac{1}{4}e^{4x} + C \\

y &= \frac{1}{4}\,{e}^{-x} + C\,{e}^{-5\,x}

\end{array}$

just reviewing some problems before Sept classes start up

I think this ok not sure how to check it with W|A

possible typos

Mahalo

https://dl.orangedox.com/wr9JnddSXWGHrASWF2

Last edited: