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The real value of m for which the substitution $y = u^{m}$ will transform the differential equation $2 x^{4} y \frac{d y}{d x} + y^{4} = 4 x^{6}$ into a homogeneous equation is

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Correct option is D

y=um⇒dydx=mum−1⋅dudx∴ Given equation ⇒2x4um⋅mum−1⋅dudx+u4m=4x6⇒dudx=4x6−u4m2mx4u2m−1For homogeneous equation degree should be same in numerator and denominator∴6=4m=4+2m−1 ⇒ m=3/2

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The real value of m for which the substitution y=um will transform the differential equation 2x4ydydx+y4=4x6 into a homogeneous equation is

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The real value of m for which the substitution $y = u^{m}$ will transform the differential equation $2 x^{4} y \frac{d y}{d x} + y^{4} = 4 x^{6}$ into a homogeneous equation is