JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

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Analyzing +4 | -1

f(x)

is differentiable function in the interoal

(0, \infty)

such that

f(1)=1

and

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

for each

x>0

, then

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

is equal to

View answer and explanation

Correct option: D

\frac{31}{18}

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

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