JEE Mains · Maths · STD 12 - 9. differential equations
Let the solution curve of the differential equation \(x \frac{d y}{d x}-y=\sqrt{y^{2}+16 x^{2}}, y(1)=3\) be \(y=y(x)\). Then \(y (2)\) is equal to
- A \(15\)
- B \(11\)
- C \(13\)
- D \(17\)
Answer & Solution
Correct Answer
(A) \(15\)
Step-by-step Solution
Detailed explanation
\(y=v x \Rightarrow \frac{d y}{d x}=v+x \frac{d v}{d x}\) \(\Rightarrow x \frac{d v}{d x}=\sqrt{v^{2}+16}\) \(\Rightarrow \int \frac{d v}{\sqrt{v^{2}+16}}=\int \frac{d x}{x}\) \(\Rightarrow \ln \left|v+\sqrt{v^{2}+16}\right|=\ln x+\ln C\)…
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