Solution of differential equation x21x2+y2(xdy+ydx)+y2(xdy−ydx)=0 is
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a
tan−1xy−12yx2=c
b
tan−1xy+12yx2=c
c
tan−1xy+13yx3=c
d
None of these
answer is C.
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Detailed Solution
Given differential equation is x21x2+y2(xdy+ydx)+y2(xdy−ydx)=0⇒x41+x2y2(xdy+ydx)+y2(xdy−ydx)=0⇒11+x2y2(xdy+ydx)+y2x2xdy−ydxx2=0⇒dtan−1xy+13dyx3=0⇒tan−1(xy)+13yx3=c