Question

Solve (y-x+1) dy - (y+x+2) dx =0

Answer 1

d[(y-x+1) y - (y+x+2)x]=0
=》d[(y^2-yx+y) - (xy+x^2+2x)]=0
=》d[y^2-xy+y - xy-x^2-2x]=0
=》y^2-x^2-2xy+y-2x=0
=》 -(x^2+y^2+2xy-y+2x)=0
=》(x+y)^2-y+2x=0
=》y=(x+y)^2+2x