MathsJEE Main 6 Apr 2026, Shift 2·Q18·MCQ·Tough

Differential Equations · Linear differential equations

Let

f : \mathbb{R} \to \mathbb{R}

be such that

f(xy) = f(x)f(y)

, for all

x, y \in \mathbb{R}

and

f(0) \neq 0

. Let

g : [1, \infty) \to \mathbb{R}

be a differentiable function such that

x^2g(x) = \int_1^x \left(t^2f(t) - tg(t)\right)dt

Then

g(2)

is equal to:

(1) $\dfrac{13}{8}$
(2) $\dfrac{11}{16}$
(3) $\dfrac{15}{32}$
(4) $\dfrac{17}{64}$

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