Question

Solve the differential equation (x^2+y^2-1)dx-2xydy=0.

Answer 1

Answer:

dyx2+y2+1=dx2xy=dy+dxx2+y2+2xy+1=dy−dxx2+y2–2xy+1⟹

d(y+x)(x+y)2+1=d(y−x)(x−y)2+1

Integrating

tan−1(y+x)−tan−1(y−x)=C′

tan−1y+x−(y−x)1+(y+x)(y−x)=C′

2x1+y2−x2=tanC′

1+y2−x2=Cx

Answer 2

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