I'm having some trouble with these, could you lend me some help?

This one for example:

y = x.y' + y'.ln(y')

I tried p = y' but all i got was this

dx + (x+ln(p))dp = 0

and then I finish with an impossible integration

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- Sep 11th 2011, 04:37 PMmafraFirst-order nonlinear ordinary differential equations
I'm having some trouble with these, could you lend me some help?

This one for example:

y = x.y' + y'.ln(y')

I tried p = y' but all i got was this

dx + (x+ln(p))dp = 0

and then I finish with an impossible integration - Sep 11th 2011, 05:18 PMchisigmaRe: First-order nonlinear ordinary differential equations
The DE requires a quite particular approach. We have...

(1)

Now if we differentiate both terms of (1) we obtain...

(2)

... and the (2) is satisfied for...

(3)

...or...

(4)

Thesystem of (1) and (3) has solution...

(5)

... and that is the general solution of (1). The system of (1) and (4) has as solution a 'particular solution' of (1) and it requires an easy procedure...

Kind regards

- Sep 11th 2011, 05:46 PMmafraRe: First-order nonlinear ordinary differential equations
Thanks, but where's the term for y'(lny')'?

I think I got the singular solution too; -e^-x - Sep 11th 2011, 06:01 PMchisigmaRe: First-order nonlinear ordinary differential equations