jee_main_2026_23_january_morning - Differential Equations Topics

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QUESTION #7 Linear Differential Equations
Let y = y(x) be the solution of the differential equation x⁴ dy + (4x³ y + 2 x)dx = 0, x > 0, y((π)/(2)) = 0. Then π⁴ y((π)/(3)) is equal to:
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QUESTION #23 Solution of Differential Equations
Let f be a twice differentiable non-negative function such that (f(x))² = 25 + ∫₀x ( (f(t))² + (f'(t))² ) dt. Then the mean of f( ₑ(1)), f( ₑ(2)), ..., f( ₑ(625)) is equal to _____.
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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)

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