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Find the real value of m for which the substitution y = u^m converts the differential equation 2x⁴ y (dy/dx) + y⁴ = 4x⁶ into a homogeneous differential equation.

1. m = 0
2. m = 1
3. m = 3/2
4. no value of m

Correct answer: m = 3/2

Solution

After substitution the three terms have degrees 2m+3, 4m and 6; setting them equal gives m = 3/2, making the equation homogeneous.

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