QJEEM24Mad036: JEE Main 2024 Mathematics - Class 12 JEEM24Mad036 Solution: Let the solution y = y ( x ) of the differential equation d y…

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QJEEM24Mad036: JEE Main 2024 Mathematics - Class 12 JEEM24Mad036 Solution: Let the solution y = y ( x ) of the differential equation d y…

Let the solution $y = y (x)$ of the differential equation $\frac{d y}{d x} - y = 1 + 4 \sin x$ satisfy $y (π) = 1$ . Then $y (\frac{π}{2}) + 10$ is equal to __________.

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Accepted Answer

$\begin{aligned} \frac{d y}{d x} - y = 1 + 4 \sin x \\ Integrating factor = e^{- \int d x} = e^{- x} \end{aligned}$

Solution is $y e^{- x} = \int (1 + 4 \sin x) e^{- x} d x$

$\begin{aligned} = - e^{- x} + 2 \cdot e^{- x} (- \sin x - \cos x) + C \\ y (π) & = 1 \Rightarrow C = 0 \end{aligned}$

Hence $y (x) = - 1 - 2 (\sin x + \cos x)$

$y (\frac{π}{2}) + 10 = 7$

QJEEM24Mad036: JEE Main 2024 Mathematics - Class 12 JEEM24Mad036 Solution: Let the solution y = y ( x ) of the differential equation d y…

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