SOLUTION: sopve the differential equation : (x^2-y^2)*dy=2xy*dx 1. dy*6x+dy(-y^2)=2x^2yd 2. 6dyx-dy^3-2x^2yd=0 3. d(6yx-y^3-2x^2y)=0 4. d=0

SOLUTION: sopve the differential equation : (x^2-y^2)dy=2xydx 1. dy*6x+dy(-y^2)=2x^2yd 2. 6dyx-dy^3-2x^2yd=0 3. d(6yx-y^3-2x^2y)=0 4. d=0

Question 964357: sopve the differential equation :
(x^2-y^2)*dy=2xy*dx
1. dy*6x+dy(-y^2)=2x^2yd
2. 6dyx-dy^3-2x^2yd=0
3. d(6yx-y^3-2x^2y)=0
4. d=0

Found 2 solutions by kekegeter , robertb:
Answer by kekegeter (97) (Show Source): You can put this solution on YOUR website!
(x^2-y^2)*dy=2xy*dx
1. dy*6x+dy(-y^2)=2x^2yd
2. 6dyx-dy^3-2x^2yd=0
3. d(6yx-y^3-2x^2y)=0
4. d=0
Hope that this will help you!
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
is an example of an Euler-homogeneous DE of degree 2.
This can be solved by the substitution x = vy.
==> dx = vdy + ydv.
==> <==>
==>
<==>
<==>
==>
==>
==>
==>
==>
==> , the general solution to the original DE.

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