JEE Advanced Differential Equations — previous year questions

21 questions from 2025, 2024, 2023, 2022, 2021, 2019, 2018, 2016, 2015, 2014, 2013, 2012, 2011, 2008.

• If y(x) is the solution of the differential equation x dy - (y² - 4y) dx = 0 for x > 0, y(1) = 2, and the…2025JEE Advanced
• Let y(x) be the solution of the differential equation x²dy/dx + xy = x² + y², x > 1/e, satisfying y(1) = 0.…2025JEE Advanced
• Let y:(-∞,∞)→(0,∞) be the solution of the differential equation dy/dx=(e⁵ˣy³+y³)/(eˣ+eˣy⁴), satisfying…2024JEE Advanced
• Let f : [1, ∞) → R be a differentiable function such that f(1) = 1/3 and 3∫₁ˣ f(t) dt = x f(x) - x³/3, x ∈…2023JEE Advanced
• For x ∈ ℝ, let y(x) be a solution of the differential equation (x²−5)dy/dx − 2xy = −2x(x²−5)² such that…2023JEE Advanced
• For x ∈ R, let the function y(x) be the solution of the differential equation dy/dx+12y=cos(π/12x), y(0)=0…2022JEE Advanced
• For any real numbers α and β, let y_(α, β)(x), x ∈ R, be the solution of the differential equation dy/dx + α…2021JEE Advanced
• Let Γ denote a curve y=y(x) which is in the first quadrant and let the point (1,0) lie on it. Let the tangent…2019JEE Advanced
• If y = y(x) satisfies the differential equation 8√x(√(9+√x))dy = (√(4+√(9+√x)))⁻¹dx, x>0 and y(0)=√7, then…2018JEE Advanced
• Let f: R → R be a differentiable function with f(0) = 1 and satisfying the equation f(x+y) = f(x)f'(y) +…2018JEE Advanced
• Let f:R→R be a differentiable function with f(0)=0. If y=f(x) satisfies the differential equation…2018JEE Advanced
• Let f:[0,∞) → R be a continuous function such that f(x) = 1 - 2x + ∫₀ˣ eˣ⁻ᵗ f(t) dt for all x ∈ [0,∞). Then,…2018JEE Advanced
• A solution curve of the differential equation (x²+xy+4x+2y+4) dy/dx-y²=0, x>0, passes through the point…2016JEE Advanced
• Let f:(0,∞)→R be a differentiable function such that f'(x)=2-f(x)/x for all x∈(0,∞) and f(1)≠ 1. Then2016JEE Advanced
• Consider the family of all circles whose centers lie on the straight line y=x. If this family of circle is…2015JEE Advanced
• Let y(x) be a solution of the differential equation (1+eˣ)y' + yeˣ = 1. If y(0)=2, then which of the…2015JEE Advanced
• The function y=f(x) is the solution of the differential equation dy/dx+xy/(x²-1)=(x⁴+2x)/(√(1-x²)) in (-1,1)…2014JEE Advanced
• A curve passes through the point (1, π/6). Let the slope of the curve at each point (x, y) be y/x + sec(y/x),…2013JEE Advanced
• If y(x) satisfies the differential equation y' - ytan x = 2xsec x and y(0) = 0, then2012JEE Advanced
• Let y'(x) + y(x) g'(x) = g(x) g'(x), y(0) = 0, x ∈ R, where f'(x) denotes df(x)/dx and g(x) is a given…2011JEE Advanced
• Let a solution y = y(x) of the differential equation x√(x² - 1) dy - y√(y² - 1) dx = 0 satisfy y(2) = 2/√3.…2008JEE Advanced

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