Let ∫₀ˣ √(1-(y^()(t))²) d t=∫₀ˣ y(t) d t, 0 ≤ x ≤ 3, y ≥ 0, y(0)=0. Then at x=2, y^()+y+1 is equal to

Differential Equations: JEE Main 2024 Mathematics question

JEE Main 2024 · 9 Apr, Evening shift · Q3566

JEE Main 20249 Apr, Evening shiftMathematicsMediumDifferential Equations163× since 2002

Let

\int_\limits0^x \sqrt{1-\left(y^{\prime}(t)\right)^2} d t=\int_0^x y(t) d t, 0 \leq x \leq 3, y \geq 0, y(0)=0

. Then at

x=2, y^{\prime \prime}+y+1

is equal to

JEE Main 2024 · 9 Apr, Evening shift · Q3566

JEE Main 20249 Apr, Evening shiftMathematicsMediumDifferential Equations163× since 2002

Let

\int_\limits0^x \sqrt{1-\left(y^{\prime}(t)\right)^2} d t=\int_0^x y(t) d t, 0 \leq x \leq 3, y \geq 0, y(0)=0

. Then at

x=2, y^{\prime \prime}+y+1

is equal to