# Find the general solution for the differential equation

• June 14th 2008, 04:51 AM
Bryn
Find the general solution for the differential equation
dy/dx - 2y.cosecx=tan(x/2) between 0<x<pi

Having some trouble with this one - I have taken e^integral of 2cosecx - which I got (tan(x/2))^2 - Then I multiplied this to all terms and I am not sure if what I'm getting is working so a full explanation would be really appreciated.

Many thanks,

Bryn
• June 14th 2008, 05:00 AM
mr fantastic
Quote:

Originally Posted by Bryn
dy/dx - 2y.cosecx=tan(x/2) between 0<x<pi

Having some trouble with this one - I have taken e^integral of 2cosecx - which I got (tan(x/2))^2 - Then I multiplied this to all terms and I am not sure if what I'm getting is working so a full explanation would be really appreciated.

Many thanks,

Bryn

Close ..... you need $e^{\int {\color{red}-}2 \, \text{cosec} \, x \, dx}$.

So the integrating factor will be $\frac{1}{\tan^2 \frac{x}{2}}$.