Differential Equations · JEE Main previous year questions

2018 1 question

1. Q162018 · 15 Apr 2018 · Shift 1

   Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}+2y=f(x)$, where $f(x)=\{\begin{array}{ll}1,& x\in [0,1]\\ 0,& \text{otherwise}\end{array}$ If $y(0)=0$, then $y\left(\frac{3}{2}\right)$ is :

   1. A.$\frac{e^2+1}{2e^4}$
   2. B.$\frac{1}{2e}$
   3. C.$\frac{e^2-1}{e^3}$
   4. D.$\frac{e^2-1}{2e^3}$
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   Answer: D