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Differential Equations question

2018 · 15 Apr · Shift 1 · Q39

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JEE Main
Mathematics
Differential Equations
2018 · 15 Apr · Shift 1 · Q39

Differential Equations question

2018 · 15 Apr · Shift 1 · Q39

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let y = y(x) be the solution of the differential equation

{{dy} \over {dx}} + 2y = f\left( x \right),

where

f\left( x \right) = \left\{ {\begin{matrix} {1,} & {x \in \left[ {0,1} \right]} \\ {0,} & {otherwise} \\ \end{matrix} } \right.

If y(0) = 0, then

y\left( {{3 \over 2}} \right)

is :

A
${{{e^2} + 1} \over {2{e^4}}}$
B
${1 \over {2e}}$
C
${{{e^2} - 1} \over {{e^3}}}$
D
${{{e^2} - 1} \over {2{e^3}}}$

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