JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution of the differential equation \(e^{x} \sqrt{1-y^{2}} d x+\left(\frac{y}{x}\right) d y=0, y(1)=-1\) Then the value of \((y(3))^{2}\) is equal to:
- A \(1+4 \mathrm{e}^{3}\)
- B \(1+4 \mathrm{e}^{6}\)
- C \(1-4 \mathrm{e}^{6}\)
- D \(1-4 \mathrm{e}^{3}\)
Answer & Solution
Correct Answer
(C) \(1-4 \mathrm{e}^{6}\)
Step-by-step Solution
Detailed explanation
\(e^{x} \sqrt{1-y^{2}} d x+\frac{y}{x} d y=0\) \(\Rightarrow e^{x} \sqrt{1-y^{2}} d x+\frac{-y}{x} d y=0\) \(\Rightarrow \int \frac{y d y}{\sqrt{1-y^{2}}}=\int x \cdot e^{x} d x\) \(\Rightarrow \int \frac{-y}{\sqrt{1-y^{2}}} d y=\int x e^{x} d x\).…
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