Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • The solution of frac{d y}{d x}+y=e^{-x}, y(0)=0 is (a) y=e^{-x}(x-1)

The solution of \frac{d y}{d x}+y=e^{-x}, y(0)=0 is
(a) y=e^{-x}(x-1)
(b) y=x e^{x}
(c) y=x e^{-x}+1
(d) y=x e^{-x}

Answers (1)

The answer is the option (d) y=x e^{-x}

Explanation: -

\frac{d y}{d x}+y=e^{-x}, y(0)=0

Here, P=1 \ and \ Q=e^{-x} I.F. =e^{\int \operatorname{ldx}}=e^{x}
 \\\therefore \text{The general solution is} \ y \cdot e^{x}=\int e^{-x} \cdot e^{x} d x+C \\\Rightarrow \quad y e^{x}=\int d x+C \\\Rightarrow y e^{x}=x+C
Given, when  x=0 and y=0
\\\Rightarrow \ 0=0+C \\ \Rightarrow \quad C=0
Eq. (i) reduces to  y \cdot e^{x}=x \ or \ y=x e^{-x}

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question