jee-main 2018 Q86

jee-main · India · 15apr 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 $f ( x ) = \left\{ \begin{array} { l l } 1 , & x \in [ 0,1 ] \\ 0 , & \text { otherwise } \end{array} \right.$. If $y ( 0 ) = 0$, then $y \left( \frac { 3 } { 2 } \right)$ is
(1) $\frac { e ^ { 2 } - 1 } { e ^ { 3 } }$
(2) $\frac { 1 } { 2 e }$
(3) $\frac { e ^ { 2 } + 1 } { 2 e ^ { 4 } }$
(4) $\frac { e ^ { 2 } - 1 } { 2 e ^ { 3 } }$

Let $y = y ( x )$ be the solution of the differential equation $\frac { d y } { d x } + 2 y = f ( x )$, where $f ( x ) = \left\{ \begin{array} { l l } 1 , & x \in [ 0,1 ] \\ 0 , & \text { otherwise } \end{array} \right.$. If $y ( 0 ) = 0$, then $y \left( \frac { 3 } { 2 } \right)$ is\\
(1) $\frac { e ^ { 2 } - 1 } { e ^ { 3 } }$\\
(2) $\frac { 1 } { 2 e }$\\
(3) $\frac { e ^ { 2 } + 1 } { 2 e ^ { 4 } }$\\
(4) $\frac { e ^ { 2 } - 1 } { 2 e ^ { 3 } }$

Paper Questions

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