JEE Mains · Maths · STD 12 - 9. differential equations
Let \(x=x(y)\) be the solution of the differential equation \(2 y \,e^{x / y^{2}} d x+\left(y^{2}-4 x e^{x / y^{2}}\right) d y=0\) such that \(x(1)=0\). Then, \(x(e)\) is equal to
- A \(e \log _{e}(2)\)
- B \(- e \log _{ e }(2)\)
- C \(e ^{2} \log _{ e }(2)\)
- D \(- e ^{2} \log _{ e }(2)\)
Answer & Solution
Correct Answer
(D) \(- e ^{2} \log _{ e }(2)\)
Step-by-step Solution
Detailed explanation
\(2 y e^{x / y^{2}} d x+\left(y^{2}-4 x e^{x / y^{2}}\right) d y=0\) \(2 e^{x / y^{2}}[y d x-2 x d y]+y^{2} d y=0\) \(2 e^{x / y^{2}}\left[\frac{y^{2} d x-x \cdot(2 y) d y}{y}\right]+y^{2} d y=0\) Divide by \(y^{3}\)…
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