JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Analyzing +4 | -1

f(x)

is a differentiable function in the interval

((0, \infty)

such that

f(a)=1

and

\lim _{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1

, for each

x > 0

, then

\mathrm{f}\left(\frac{3}{2}\right)

is equal to:

View answer and explanation

Correct option: D

\frac{31}{18}

Option D (

\frac{{31}}{{18}}

) is correct because it is the value of f(3/2) obtained after solving the given differential equation and using the initial condition f(a) = 1.

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y=y(x)

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y=y(t)

\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}

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