Question

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.
A. m=0
B. m=1
C. `m=3/2`
D. `m=2/3`

Answer 1

Correct Answer - c
` y = u^(m) rArr (dy)/(dx) = mu^(m-1) (du)/(dx)`
Hence, ` 2x^(4) * u^(m) * mu^(m-1) * (du)/(dx) +u^(4m) = 4x^(6)`
` (du)/(dx) = (4x^(6)-u^(4m))/(2mx^(4)u^(2m-1))`
` rArr 4m = 6 rArr = 3/2`
` rArr 4m = 6rArr m = 3/2 `