JEE Mains · Maths · STD 12 - 9. differential equations
Let the solution \(y=y(x)\) of the differential equation \(\frac{d y}{d x}-y=1+4 \sin x\) satisfy \(y(\pi)=1\). Then \(y\left(\frac{\pi}{2}\right)+10\) is equal to ...........
- A \(10\)
- B \(8\)
- C \(7\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(7\)
Step-by-step Solution
Detailed explanation
\( y e^{-x}=\int\left(e^{-x}+4 e^{-x} \sin x\right) d x \) \( y e^{-x}=-e^{-x}-2\left(e^{-x} \sin x e^{-x} \cos x\right)+C \) \( y=-1-2(\sin x+\cos x)+c e^x \) \( \because y(\pi)=1 \Rightarrow c=0 \) \( y(\pi / 2)=-1-2=-3 \) \( \text { Ans }=10-3=7\)
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