JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

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Application +4 | -1

The solution of the differential equation

\frac{d^2 y}{d x^2}=e^x\sin x

when

y_1\left(\frac{\pi}{4}\right)=0, y\left(\frac{\pi}{2}\right)=0

View answer and explanation

Correct option: D

y=(1 / 2) e^x \sin (x-\pi / 2)

The correct answer is D (

y=(1 / 2) e^x \sin (x-\pi / 2)

) because it satisfies the given differential equation and the initial conditions

y_1(\frac{\pi}{4})=0, y(\frac{\pi}{2})=0

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\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}

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\lim \limits_{{x \rightarrow \infty}} y(t)