Help with solving a first order linear and first order non-linear

Xyius
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Here is an image of the first order linear differential equation and my attempt to solve it. It ends in an integral that can not be solved.

http://img831.imageshack.us/img831/9937/math1.gif

And here is an image of the first order non-linear differential equation and my attempt to solve it. This one leads to a non-separable differential equation after a substitution.

http://img215.imageshack.us/img215/4893/math2.gif

Any advise?
 
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You have:

(1-y)dx+xydy=0

You can find the 1/M(M_y-N_x) integrating factor for that.
 
jackmell said:
You have:

(1-y)dx+xydy=0

You can find the 1/M(M_y-N_x) integrating factor for that.

The integrating factor isn't working. I was under the impression you can only use the integrating factor only when the two partials differ by a constant only, which they do not. :\
 
Separable ODE :
 

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y(x) cannot be expressed in terms of a finite number of elementary functions. The closed form requires a special function :
 

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