The discussion focuses on solving the homogeneous differential equation represented by y²dx - x(2x + 3y)dy = 0. The user successfully transformed the equation into a homogeneous form and attempted a substitution with x = uy, leading to the equation y²udy + y³du - 2x²dy + 3yxdy = 0. The conversation highlights the equivalence of the substitution methods x = uy and y = ux, and suggests dividing the resulting equation by x² for simplification.
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I am more accustomed to write y= ux but your method is equivalent.mamma_mia66 said: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.