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Find the general solution of the differential equation x²*(y')² + x*y*y' - 6y² = 0, where y' = dy/dx.
- y = Cx²
- x² y = C
- (1/2) ln y = C + log x
- x³ y = C
Correct answer: y = Cx²
Solution
Solving the quadratic gives x*y' = 2y or x*y' = -3y; integration yields y = Cx² (and y = C/x³). Among the options, y = Cx² is the valid solution.
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