If $\int_a^x t y(t) d t=x^2+y(x)$, then $y$ as a function of $x$ is

$y=2-\left(1+a^2\right) e^{\frac{x^2-a^2}{2}}$

JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Application +4 | -1

\int_a^x t y(t) d t=x^2+y(x)

, then

y

as a function of

x

View answer and explanation

Correct option: A

y=2-\left(2+a^2\right) e^{\frac{x^2-a^2}{2}}

Option A,

y=2-(2+a^2) e^{\frac{x^2-a^2}{2}}

, is the correct function

y

as a function of

x

obtained by solving the given integral equation.

Practice All Chapter MCQs →

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\alpha>0, \beta>0

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\lim \limits_{{x \rightarrow \infty}} y(t)