JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution of the differential equation \(\left(3 y^2-5 x^2\right) y d x+2 x\left(x^2-y^2\right) d y=0\) such that \(y(1)=1\). then \(\left|(y(2))^3-12 y(2)\right|\) is equal to:
- A \(32 \sqrt{2}\)
- B \(64\)
- C \(16 \sqrt{2}\)
- D \(32\)
Answer & Solution
Correct Answer
(A) \(32 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(\left(3 y^2-5 x^2\right) y \cdot d x+2 x\left(x^2-y^2\right) d y=0\) \(\Rightarrow \frac{d y}{d x}=\frac{y\left(5 x^2-3 y^2\right)}{2 x\left(x^2-y^2\right)}\) Put \(y = mx\) \(\Rightarrow m + x \cdot \frac{ dm }{ dx }=\frac{ m \left(5-3 m ^2\right)}{2\left(1- m ^2\right)}\)…
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