NDA 2017 Maths · Mathematics · Differential Equations · medium

If y(x) satisfies dy/dx+y=e^-x with y(0)=1, then y(1) equals

Single correct option

y(x)

satisfies

\dfrac{dy}{dx}+y=e^{-x}

with

y(0)=1

, then

y(1)

equals

Show answer and solution

Answer: (A) $\frac2e$

The integrating factor is

e^x

, so

\frac{d}{dx}(ye^x)=1

and

ye^x=x+C

. From

y(0)=1

C=1

, hence

y=(x+1)e^{-x}

and

y(1)=\frac2e

. Without the constant

C=1

one would get

\frac1e

Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake