Solving the Homogeneous Equation y2dx -x(2x+3y)dy =0

[mamma_mia66]

Homework Statement

y²dx -x(2x+3y)dy =0 I have to recognize the equation and solve it

Homework Equations

The Attempt at a Solution

I did y²dx - (2x²+ 3yx) dy=0
which is a homogeneous now
after I substitude x=uy
dx=udy + ydu

I stuck here after the substitution

y²udy+y³du - 2x²dy + 3yxdy=0

please someone help if I am not in right direction from the begining.

 

[HallsofIvy]

Homework Statement

y²dx -x(2x+3y)dy =0 I have to recognize the equation and solve it

Homework Equations

The Attempt at a Solution

I did y²dx - (2x²+ 3yx) dy=0
which is a homogeneous now
after I substitude x=uy
dx=udy + ydu

I stuck here after the substitution

y²udy+y³du - 2x²dy + 3yxdy=0

please someone help if I am not in right direction from the begining.

I am more accustomed to write y= ux but your method is equivalent.
Saying x= uy is the same as saying u= y/x. Divide your last equation by $x^2$ and see what you get!

 

[mamma_mia66]

ok, thanks.