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Consider the homogeneous differential eq...

Consider the homogeneous differential equation `(dy)/(dx)=f((y)/(x))` By putting `(y)/(x)=v`, the equation reduces to `(dv)/(f(v)-v)=(dx)/(x)`. Integrating we get `int(dv)/(f(v)-v)=int(dx)/(x)+c`
Solution of `x(x-y)dy+y^(2)dx=0` is-

A

`y^(2)=c^(2)e^((2y)/(x))`

B

`y=ce^((2y)/(x))`

C

`y^(2)=ce^((y)/(2x))`

D

`y^(2)=c^(2)e^((y^(2))/(x))`

Text Solution

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The correct Answer is:
A
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