Check out some similar questions!

Wikkibahi · Nov 29, 2011, 12:46 AM

I attach the Math File. Please Open it and Solve my Problem.
Please tell me as soon as possible.
Please explain me with step by step...!
Thanks a lot for this...!

Aurora2000 · Nov 29, 2011, 01:47 AM

$\frac{dy}{dx}+P(x)y=Q(x)$

Multiply both sides by $e^{\int P(x)dx}$ :
$\frac{dy}{dx}e^{\int P(x)dx}+P(x)ye^{\int P(x)dx}=Q(x)e^{\int P(x)dx}$

Use product rule on left hand side:
$\frac{dy}{dx}e^{\int P(x)dx}+P(x)ye^{\int P(x)dx}=\frac{d}{dx}(ye^{\int P(x)dx})$

Thus integrating on both sides

$\frac{d}{dx}(ye^{\int P(x)dx})=Q(x) e^{\int P(x)dx}+C$ .

Aurora2000 · Nov 29, 2011, 01:51 AM

Delete the last C in the above post (typo), integrating

$\frac{d}{dx}(ye^{\int P(x)dx})=Q(x)e^{\int P(x)dx}$

leads to

$y e^{\int P(x)dx}=\int Q(x)e^{\int P(x)dx} dx +C$