Question

the solution curves to the DE 2xyy' = y²-x²

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Answer 1

Answer:

#hope it help u

Step-by-step explanation:

[tex]dy=2xyy2−x2

Substitute y=vx

∴v+xdxdv=2vv2−1⇒xdxdv=−2v1+v2⇒1+v22vdv+xdx=0

Integrating log(1+v2)+logx=logk

∴x(1+v2)=k.

Substitute v=xy

⇒x2+y2=kx.