If the general solution of d y d x = y^2 x y-y^2-x^2 is ⁻¹ ( y x )=f(y)+C , then f (e^3 )=

Step-by-step solution

On putting y=m x aligned & m+x d m d x = m^2 m-m^2-1 & x d m d x = m^3+m m-m^2-1 & m-m^2-1 m^3+m d m= d x x & ( 1 m^2+1 - 1 m ) d m= |x|+C & ⁻¹ ( y x )- | y x |= |x|+C & ⁻ ( y x )= |y|+C & f(y)= |y| & f (e^3 )= |e^3 |=3 aligned