QJEEM24Ma5306: JEE Main 2024 Mathematics - Class 12 JEEM24Ma5306 Solution: Let ∫ 0 x 1 − ( y ′ ( t ) ) 2 d t = ∫ 0 x y ( t ) d t , 0 ≤ x ≤ …

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QJEEM24Ma5306: JEE Main 2024 Mathematics - Class 12 JEEM24Ma5306 Solution: Let ∫ 0 x 1 − ( y ′ ( t ) ) 2 d t = ∫ 0 x y ( t ) d t , 0 ≤ x ≤ …

Let $\int_{0}^{x} \sqrt{1 - {(y^{'} (t))}^{2}} d t = \int_{0}^{x} y (t) d t, 0 \leq x \leq 3, y \geq 0, y (0) = 0$ . Then at $x = 2, y^{''} + y + 1$ is equal to

Multiple Choice Options

A 2
B 2
C `1/2
D 1

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Accepted Answer

$\int_{0}^{x} \sqrt{1 - {(y^{'} (t))}^{2}} d t = \int_{0}^{x} y (t) d t$

Differentiating both side

$\begin{aligned} \sqrt{1 - {(y^{'} (x))}^{2}} = y (x) \\ {(\frac{d y}{d x})}^{2} + y^{2} = 1 \\ y^{' 2} + y^{2} = 1 \\ 2 y^{'} y^{''} + 2 y y^{'} = 0 \\ y^{''} + y = 0 \end{aligned}$

$∴$ JEE Main 2024 (Online) 9th April Evening Shift Mathematics - Differential Equations Question 33 English Explanation

QJEEM24Ma5306: JEE Main 2024 Mathematics - Class 12 JEEM24Ma5306 Solution: Let ∫ 0 x 1 − ( y ′ ( t ) ) 2 d t = ∫ 0 x y ( t ) d t , 0 ≤ x ≤ …

Multiple Choice Options

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