JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Application +4 | -1

For the differential equation

\frac{d y}{d x}+i y=2 \sin (x)

, with initial condition

y(0)=\frac{3}{2}

. If

y(\pi)=\frac{a}{b}+c \pi i

, for co-prime integers

a

and

b

, find

a b c

. [

i=\sqrt{-1}

denotes the imaginary unit.]

View answer and explanation

Correct option: A

Option A (6) is correct because solving the given differential equation with the initial condition and substituting

x = \pi

yields

y(\pi) = -\frac{3}{2} - \pi i

, leading to

abc = 6

More Questions from DIFFERENTIAL EQUATIONS

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y=y(x)

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y=y(t)

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

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