Let a curve y = f(x) pass through the point (2, (log e 2)²) and have slope 2y x log e x for all positive real value of x. Then the value of f(e) is equal to _ _ _ _ _ _ _.

Differential Equations: JEE Main 2021 Mathematics question

JEE Main 2021 · 25 Jul, Evening shift · Q32

JEE Main 202125 Jul, Evening shiftMathematicsMediumDifferential Equations163× since 2002

Let a curve y = f(x) pass through the point (2, (log_e2)²) and have slope

{{2y} \over {x{{\log }_e}x}}

for all positive real value of x. Then the value of f(e) is equal to ______________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 · 25 Jul, Evening shift · Q32

JEE Main 202125 Jul, Evening shiftMathematicsMediumDifferential Equations163× since 2002

Let a curve y = f(x) pass through the point (2, (log_e2)²) and have slope

{{2y} \over {x{{\log }_e}x}}

for all positive real value of x. Then the value of f(e) is equal to ______________.

Your answerType your answer. Integers and decimals are accepted.