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Question

Solve the differential equation x2dy+y(x+y)dx=0, given that y=1 when x=1.

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Solution

x2dy+(yx+y2)dx=0
dydx+yx+(yx)2=0 yx=x
v+xdvdx+v+v2=0 dydx=v+xdvdx
xdvdx=(v2+2v)
dv(v+2)=dxx12v+2v(v+2)v=dxx
12(1v1v+2)dv=dxx12ln(vv+2)=lmx+c
12ln(yy+2x)=lnx+c

1208694_1167654_ans_b4502a8a7c2149d1a358fb64643e8749.jpg

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