jee_main_2025_02_april_evening - Differential Equations Topics

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QUESTION #52 Linear Differential Equations
Let f:[1,∞) → [2,∞) be a differentiable function. If 10∫₁xf(t)dt = 5xf(x) - x⁵ - 9 for all x ≥ 1, then the value of f(3) is:
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QUESTION #71 First Order Linear Differential Equations
Let y = y(x) be the solution of the differential equation (dy)/(dx) + 2y ² x = 2 ² x + 3 x · ² x such that y(0) = (5)/(4). Then 12(y((π)/(4)) - e⁻²) 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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