JEE Mains · Maths · STD 12 - 9. differential equations
If the solution of the differential equation \(\frac{d y}{d x}+e^{x}\left(x^{2}-2\right) y=\left(x^{2}-2 x\right)\left(x^{2}-2\right) e^{2 x} \quad\) satisfies \(y(0)=0\), then the value of \(y(2)\) is
- A \(-1\)
- B \(1\)
- C \(0\)
- D \(e\)
Answer & Solution
Correct Answer
(C) \(0\)
Step-by-step Solution
Detailed explanation
\(\text { I.F. }=e^{\int e^{x}\left(x^{2}-2\right) d x}=e^{\int e^{x}\left(x^{2}-2 x+2 x-2\right)} d x\) \(=e^{e^{x}\left(x^{2}-2 x\right)}\)…
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