Find the real value of `m` for which the substitution `y=u^m` will transform the differential equation `2x^4y(dy)/(dx)+y^4=4x^6` in to a homogeneous equation.

Explanation

`y=u^(m)`
or `(dy//dx) = mu^(m-1)(du)/(dx)`
The given differential equation becomes
`2x^(4).u^(m). Mu^(m-1)(du)/(dx) +u^(4m)=4x^(6)`
for homogenous equation, degree of each term should be same in the numerator and the denominator. Hence,
`6=4m=4+2m-1` or `m=3//2`