JEE Main Mathematics — Differential Equations Previous-Year Questions

Let f be a twice differentiable non-negative function such that (f(x))²=25+∫₀x ((f(t))²+ (fⁱme(t) )² ) dt. Then the mea…

Let y=y(x) be the solution of the differential equation: (dy)/(dx)+ (6x²+(3x²+2x³+4)e⁻²x(x³+2)(2+e⁻²x) )y=2+e⁻²x, x (-1…

If the solution curve y=f(x) of the differential equation (x²-4 ) yⁱme-2 x y+2 x (4-x² )²=0, x>2, passes through the po…

Let y=y(x) be the solution of the differential equation x ~d y~d x-y=x² x, x (0, π). If y ((π)/(2) )=(π)/(2), then 6 y…

Let f:[1, ∞) → R be a differentiable function. If 6 ∫₁x f(t) d t=3 x f(x)+x³-4 for all x ≥ 1, then the value of f(2)-f(…

Let y=y(x) be the solution of the differential equation x√(1-x²) dy + (y√(1-x²) - x⁻¹x )dx = 0, x (0, 1), → ₁^₋ y(x) =…

If y=y(x) satisfies the differential equation 16(x+9 √(x))(4+9+√(x)) y ~d y=(1+2 y) d x, x>0 and y(256)=(π)/(2), y(49)=…

Let y=y(x) be the solution of the differential equation x (d y)/(d x)- 2 y=x³ (2-x³ ) ² y, x ≠ 0. If y(2)=0, then (y(1)…

Let y = y(x) be the solution of the differential equation (dy)/(dx) = (1 + x + x²)(1 - y + y²), y(0) = (1)/(2). Then (2…

Let y=y(x) be a differentiable function in the interval (0, ∞) such that y(1)=2, and t → x (t² y(x)-x² y(t)x-t )=3 for…