JEE Mains · Maths · STD 12 - 9. differential equations
The general solution of the differential equation \((y^2 -x^3) dx -xydy = 0\, (x \ne 0)\) is (where \(c\) is a constant of integration)
- A \(y^2 + 2x^3 + cx^2 = 0\)
- B \(y^2 -2x^3 + cx^2 = 0\)
- C \(y^2 + 2x^2 + cx^3 = 0\)
- D \(y^2 -2x^2 + cx^3 = 0\)
Answer & Solution
Correct Answer
(B) \(y^2 -2x^3 + cx^2 = 0\)
Step-by-step Solution
Detailed explanation
\(\left(y^{2}-x^{3}\right) d x-x y d y=0 \quad x \neq 0\) \(\Rightarrow y^{2}-x^{3}-x y \frac{d y}{d x}=0\) or, \(x y \frac{d y}{d x}-y^{2}=-x^{3}\) \(y \frac{d y}{d x}-\frac{1}{x} y^{2}=-x^{2}\) ........\((i)\) Let \(y^{2}=\mu\) \(2 y \frac{d y}{d x}=\frac{d \mu}{d x}\) Putting…
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