JEE Main 2025 — Differential Equations Questions with Solutions

Let y=y(x) be the solution of the differential equation (x²+1 ) yⁱme-2 x y= (x⁴+2 x²+1 ) x, y(0)=1. Then ∫₋₃³ y(x) d x…

Let f(x)=x-1 and g(x)=e^x for x R. If (d y)/(d x)= (e⁻² √⁽x⁾ g(f(f(x)))-y√(x) ), y(0)=0, then y(1) is :-

Let x=x(y) be the solution of the differential equation y² ~d x+ (x-(1)/(y) ) d y=0. If x(1)=1, then x ((1)/(2) ) is :

If for the solution curve y=f(x) of the differential equation d y~d x+( x) y=(2+ x)/((1+2 x)²), x ((-π)/(2), (π)/(2) ),…

Let y=y(x) be the solution curve of the differential equation x (x²+e^x ) d y+ (e^x(x-2) y-x³ ) d x=0, x 0 passing thro…

Let f be a differentiable function such that 2(x+2)² f(x)-3(x+2)²=10 ∫₀^x(t+2) f(t) d t, x ≥ 0. Then f(2) is equal to _…

If a curve y=y(x) passes through the point (1, (π)/(2) ) and satisfies the differential equation (7 x⁴ y-e^x cosec y )…

If y=y(x) is the solution of the differential equation, √(4-x²) ~d y~d x= ( ( ⁻¹ ((x)/(2) ) )²-y ) ⁻¹ ((x)/(2) ),-2 ≤ x…

Let a curve y=f(x) pass through the points (0,5) and ( e 2, k ). If the curve satisfies the differential equation 2(3+y…

Let g be a differentiable function such that ∫₀^x g(t) d t=x-∫₀^x tg(t) d t, x ≥ 0 and let y=y(x) satisfy the different…