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Solve the following differential equation. (x-y)^2 dx + 2xy dy =0

Solve the following differential equation. (x-y)^2 dx + 2xy dy =0

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 years ago
 (x-y)2 dx + 2xy dy=0 
(x-y)2=-2xydy/dx 
let dy/dx=y1 
=-2xyy1 
y1=-(x-y)2/2xy 
=-(1+(y/x)2-2(y/x))/2(y/x) 
Let y/x=u 
=-(1+u2-2u)/2u 
Whenever y/x=u,y=xu,y1=u1x+u 
Presently, u1x+u=1+u2/u 
=1/u+u/2 
u1x=1/u-u/2=2-u2/2u .

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