# Thread: linear ordinary differential equations

1. ## linear ordinary differential equations

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

2. That is correct. You can check it by observing that $\displaystyle y'=ce^x$ so $\displaystyle y'-y = ce^x - (ce^x - 2) = 2$.

3. Originally Posted by anderson
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) $\displaystyle \frac{dy}{dx} -y=2$
$\displaystyle \int\frac{dy}{y+2}=\int dx+c'$
$\displaystyle y+2=ce^x$
That is correct. Just FYI that particular DE is known as a seperable differential equation.