Equation is .

I have tried to substitute and I am stuck at

To be exact I do not know where to go from there in calculus sense.

Printable View

- Dec 2nd 2011, 11:17 AMlosm1Homogeneous ODE
Equation is .

I have tried to substitute and I am stuck at

To be exact I do not know where to go from there in calculus sense. - Dec 2nd 2011, 12:07 PMDarkprinceRe: Homogeneous ODE
So you have (1/x)dx = -(1/(vlnv-v) )dv= -1/(v(lnv-1)

Now the integral of -1/(v(lnv-1) is -ln(lnv - 1)

Then proceed accordingly, hope I helped :) - Dec 2nd 2011, 12:08 PMalexmahoneRe: Homogeneous ODE
- Dec 3rd 2011, 03:19 AMlosm1Re: Homogeneous ODE
In my example differentials dx and dv are in denominator:

I'm having trouble applying your formula in this case. Can you please clarify further? - Dec 3rd 2011, 04:13 AMProve ItRe: Homogeneous ODE
- Dec 3rd 2011, 05:17 AMDarkprinceRe: Homogeneous ODE
- Dec 3rd 2011, 09:47 AMtom@ballooncalculusRe: Homogeneous ODE
Yes, that is the idea. However, just in case an overview helps...

http://www.ballooncalculus.org/draw/double/five.png

http://www.ballooncalculus.org/draw/double/fivea.png

http://www.ballooncalculus.org/draw/double/fiveb.png

... where (key in spoiler) ...

__Spoiler__:

__________________________________________________ __________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!