JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution of the differential equation \(\left(x^2+1\right) y^{\prime}-2 x y=\left(x^4+2 x^2+1\right) \cos x\), \(y(0)=1\). Then \(\int_{-3}^3 y(x) d x\) is :
- A 24
- B 36
- C 30
- D 18
Answer & Solution
Correct Answer
(A) 24
Step-by-step Solution
Detailed explanation
\begin{aligned} & \left(x^2+1\right) \frac{d y}{d x}-2 x y=\left(x^4+2 x^2+1\right) \cos x \\ & \frac{d y}{d x}-\left(\frac{2 x}{x^2+1}\right) y=\frac{\left(x^2+1\right)^2 \cos x}{\mathrm{cx}^2+1}=\left(\mathrm{x}^2+1\right) \cos x \\ & \text { (Linear D.E) } \\ & P=\frac{-2…
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