Let f be a differentiable function such that x²f(x) - x = 4∫₀ˣ tf(t)dt, f(1) = 2/3. Then 18f(3) is equal to:

Differential Equations: JEE Main 2023 Mathematics question

JEE Main 2023 · 10 Apr, Morning shift · Q3561

JEE Main 202310 Apr, Morning shiftMathematicsMediumDifferential Equations163× since 2002

Let

f

be a differentiable function such that

{x^2}f(x) - x = 4\int\limits_0^x {tf(t)dt}

f(1) = {2 \over 3}

. Then

18f(3)

is equal to :

JEE Main 2023 · 10 Apr, Morning shift · Q3561

JEE Main 202310 Apr, Morning shiftMathematicsMediumDifferential Equations163× since 2002

Let

f

be a differentiable function such that

{x^2}f(x) - x = 4\int\limits_0^x {tf(t)dt}

f(1) = {2 \over 3}

. Then

18f(3)

is equal to :