NDA 2024 Maths · Mathematics · Differential Equations · medium

The solution of dy/dx=2xy satisfying y(0)=1 takes the value ____ at x=1.

Single correct option

The solution of

\dfrac{dy}{dx}=2xy

satisfying

y(0)=1

takes the value ____ at

x=1

Show answer and solution

Answer: (B) $e$

Separate variables:

\frac{dy}{y}=2x\,dx

, so

\ln y=x^2+C

. Since

y(0)=1

C=0

and

y=e^{x^2}

. Hence

y(1)=e

. Trap: integrating

2x

2x^2

gives

e^2

, and forgetting the initial condition leaves an undetermined constant.

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