Solve `(d^2y)/(dx^2)=((dy)/(dx))^2`

Explanation

`(d^(2)y)/(dx^(2))=((dy)/(dx))^(2)`
or `d/(dx)(dy)/(dx) = ((dy)/(dx))^(2)`
or `(d(dy)/(dx))/((dy)/(dx))=(dy)/(dx)dx`
or `int ((d(dy)/(dx)))/((dy)/(dx))=intdy`
`therefore log(dy)/(dx)=logy+logC_(1)`
`therefore (dy)/(dx)=C_(1)y`
`therefore (dy)/(y)=C_(1)dx`
`therefore int(dy)/(y) = C_(1)intdx`
`therefore logy=C_(1)x+k`
`therefore y=e^(C_(1)x+k)=C_(2)e^(C_(1)x)`