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

[Xyius]

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?

 

[jackmell]

You have:

$$(1-y)dx+xydy=0$$

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

 

[Xyius]

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. :\

 

[JJacquelin]

Separable ODE :

 

[JJacquelin]

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