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Solve: (dy)/(dx) = (yf^(')(x)-y^(2))/(...

Solve:
`(dy)/(dx) = (yf^(')(x)-y^(2))/(f(x))`

Text Solution

Verified by Experts

We have, `(dy)/(dx) = (yf^(')(x)-y^(2))/(f(x))`
`therefore yf^(')(x)dx-f(x)dy=y^(2)dx`
`rArr (yf^(')(x)dx-f(x)dy)/(y^(2))=dx`
`d[f(x)/(y)]=dx`
On integrating, we get
`(f(x))/(y) = x+c` or `f(x) = (x+c)y`
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