reducible differential equation

[Sonal7]

Hello againView attachment 18870
I dont seem to be able to the work through a question.

Here is my working:
[MATH]y=ux[/MATH][MATH]dy/dx =du/dx *x+ u[/MATH]

[MATH]dy/dx=(x^2+y^2)/xy[/MATH](1)
Substituting in (1)
[MATH]du/dx*x+u=\frac{(x^2+U^2x^2)}{x^2u}[/MATH][MATH]du/dx *x +u = \frac{x^2}{x^2u} +\frac{U^2x^2}{x^2u}[/MATH]
[MATH]du/dx *x = \frac{1}{u}[/MATH]
integrating both sides gives:
[MATH]x=lnu[/MATH]This gives
[MATH]ln \frac{y}{x}=x[/MATH]

I am now stuck! i cant seem to fit any of the ans. Please help.

 

[LCKurtz]

Hello againView attachment 18870

[MATH]du/dx *x = \frac{1}{u}[/MATH]

It's OK to here.

integrating both sides gives:
[MATH]x=lnu[/MATH]

That last step is wrong. You need to separate variables: [MATH]u du = \frac{dx} x[/MATH], then integrate.

 

[Sonal7]

Thank you so much. I got the right ans.