# Separable Partial ODE

• Nov 4th 2008, 05:37 AM
BSc
Separable Partial ODE
Find the general solution of:

x.du/dx - (1/2).y.du/dy=0

I know that for it to be separable u(x,y)=X(x)Y(y)

so:

x.Y(y)dX/dx + (1/2).X(x)dY/dy = 0

which cancels to:

x/X(x).(dX/dx) = - y/2Y(y).dY/dy

so:

X(x) = -c. Y(y) c is some constant

so:

x/X(x).dX/dx = c
y/2Y(y).dY/dy=c

from here i am stuck. Any help appreciated
Thanks
• Nov 4th 2008, 07:44 PM
mr fantastic
Quote:

Originally Posted by BSc
Find the general solution of:

x.du/dx - (1/2).y.du/dy=0

I know that for it to be separable u(x,y)=X(x)Y(y)

so:

x.Y(y)dX/dx + (1/2).X(x)dY/dy = 0

which cancels to:

x/X(x).(dX/dx) = - y/2Y(y).dY/dy

so:

X(x) = -c. Y(y) c is some constant

so:

x/X(x).dX/dx = c
y/2Y(y).dY/dy=c

from here i am stuck. Any help appreciated
Thanks

The two ordinary DE's can be re-arranged into a form where the relevance of Integrating factor - Wikipedia, the free encyclopedia should be obvious.

Do you need to worry about whether c is positive, negative or zero ......?