# Thread:

1. ## 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

2. 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 $\frac{1}{\tan^2 \frac{x}{2}}$.
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