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Q.

The solution of the D.E yy1=x y2x2+fy2x2f1y2x2 is

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a

fy2/x2=cx2

b

x2fy2/x2=c2y2

c

x2fy2/x2=c

d

fy2/x2=cy/x

answer is A.

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Detailed Solution

yxdydx=y2x2+f y2x2f1y2x2 Put y=vxdydx=v+xdvdx→vv+xdvdx=v2+fv2f1v2→vxdvdx=fv2f1v2∫f1v2 2v dvfv2=2∫dxx→ln fv2=ln x2+ln c→fv2=cx2→fy2x2=cx2

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