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Solve the differential equation x² (y')² + x y y' - 6 y² = 0, where y' = dy/dx. Which of the following are solutions?
- y = C x²
- x² y = C
- (1/2) ln y = C + ln x
- x³ y = C
Correct answer: y = C x²
Solution
Factoring the quadratic in y' gives y' = 2y/x (-> y = C x²) and y' = -3y/x (-> x³ y = C); both families are solutions.
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