NDA 2024 Maths · Mathematics · Differential Equations · medium

The solution of dy/dx+2y=0 with y(0)=3 takes the value ____ at x=ln 2.

Single correct option

The solution of

\dfrac{dy}{dx}+2y=0

with

y(0)=3

takes the value ____ at

x=\ln2

Show answer and solution

Answer: (C) $\frac34$

Separating variables,

y=Ce^{-2x}

and

y(0)=3

gives

C=3

. At

x=\ln2

y=3e^{-2\ln2}=3\cdot\frac14=\frac34

. Trap:

\frac32

uses

e^{-\ln2}

(one factor of 2), and

\frac3{e^2}

substitutes

x=1

rather than

\ln2

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