QJEEM19Ma989c: JEE Main 2019 Mathematics - Class 12 JEEM19Ma989c Solution: The general solution of the differential equation (y 2 – x 3…

Question

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The general solution of the differential equation (y² – x³)dx – xydy = 0 (x

\neq

0) is : (where c is a constant of integration)

Accepted Answer

(y^{2} - x^{3}) d x - x y d y = 0

\Rightarrow y (y d x - x d y) = x^{3} d x

\Rightarrow \frac{y}{x} (\frac{y d x - x d y}{x^{2}}) = d x

\Rightarrow - \frac{y}{x} d (\frac{y}{x}) = d x

\Rightarrow - \frac{1}{2} {(\frac{y}{x})}^{2} = x + k

\Rightarrow - y^{2} = 2 x^{3} + 2 x^{2} k

\Rightarrow y^{2} + 2 x^{3} + c x^{2} = 0

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