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For which actual value of n will the change of variable y = uⁿ convert the differential equation 2x⁴ y (dy/dx) + y⁴ = 4x⁶ into a homogeneous equation?
- 1/2
- 1
- 3/2
- 2
Correct answer: 3/2
Solution
Choosing n = 3/2 allows the substitution y = u^(3/2) to balance the degrees of the terms in the differential equation, transforming it into a homogeneous equation where all terms can be expressed as a function of u and its derivatives.
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