Hi everyone

Need help to verify this workings, thank you in advance for qall your help & support.

Solve the following linear ordinary differential equations

i) $\displaystyle \frac{dy}{dx} -y=2$

$\displaystyle \int\frac{dy}{y+2}=\int dx+c'$

$\displaystyle y+2=ce^x$

ii) $\displaystyle \frac{dy}{dx} + 5y=e^{-2x}$

Integral factor

$\displaystyle e^{\int5dx}=e^{5x}$

Multiply by U.F & integrate

$\displaystyle e^{5x}.y=\int e^{5x}.e^{-2x}dx + c$]

$\displaystyle ye^{5x}=\frac{1}{3}e^{3x}+c$ or

$\displaystyle y = \frac{1}{3}e^{-2x}+ce^{-5x}$