jee-main 2018 Q86

jee-main · India · 15apr_shift1 First order differential equations (integrating factor)
Let $y = y ( x )$ be the solution of the differential equation $\frac { d y } { d x } + 2 y = f ( x )$, where
$$f ( x ) = \left\{ \begin{array} { l c } 1 , & x \in [ 0,1 ] \\ 0 , & \text { otherwise } \end{array} \right.$$
If $y ( 0 ) = 0$, then $y \left( \frac { 3 } { 2 } \right)$ is
(1) $\frac { e ^ { 2 } - 1 } { 2 e ^ { 3 } }$
(2) $\frac { e ^ { 2 } - 1 } { e ^ { 3 } }$
(3) $\frac { 1 } { 2 e }$
(4) $\frac { e ^ { 2 } + 1 } { 2 e ^ { 4 } }$
Let $y = y ( x )$ be the solution of the differential equation $\frac { d y } { d x } + 2 y = f ( x )$, where

$$f ( x ) = \left\{ \begin{array} { l c } 
1 , & x \in [ 0,1 ] \\
0 , & \text { otherwise }
\end{array} \right.$$

If $y ( 0 ) = 0$, then $y \left( \frac { 3 } { 2 } \right)$ is\\
(1) $\frac { e ^ { 2 } - 1 } { 2 e ^ { 3 } }$\\
(2) $\frac { e ^ { 2 } - 1 } { e ^ { 3 } }$\\
(3) $\frac { 1 } { 2 e }$\\
(4) $\frac { e ^ { 2 } + 1 } { 2 e ^ { 4 } }$