The differential equation `(dy)/(dx)+(y^(2))/(x^(2))=(y)/(x)` has the solution

Options

A. `x=y(logx+C)`
B. `y=x(logy+C)`
C. `x=(y+C)logx`
D. `y=(x+C)logy`

Answer

A

Explanation

We have, `(dy)/(dx)+(y^(2))/(x^(2))=(y)/(x)`
Putting `y=vx` and `(dy)/(dx)=v+x(dv)/(dx)`, we get
`v+x(dv)/(dx)+v^(2)=v rArr x(dv)/(dx)=-v^(2)rArr-(1)/(v^(2))dv=(1)/(x)dx`
On integrating, we get
`(1)/(v)=log x+C rArr x=y(logx+C)`