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If the relation x^k + y^k = α^k holds for positive constants k and α, and the differential equation dy/dx + (y/x)^(1/3) = 0 is satisfied, then the value of k is:
- 3/2
- 4/3
- 2/3
- 1/3
Correct answer: 2/3
Solution
The differential equation can be solved using separation of variables, leading to a relationship between x and y that matches the form of the given relation. By analyzing the resulting expressions, it can be shown that the exponent k must equal 2/3 to satisfy the equation.
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