GATE Ordinary Differential Equations: Higher Order Equations and Systems – Previous Year Questions
10 GATE previous year questions on Higher Order Equations and Systems (Ordinary Differential Equations, Mathematics) with answers and explanations, from every paper.
- GATE 2021 MA Q30 – For x²y″−4xy′+6y=0,x>0, with y(2)=0,y′(2)=4, find y(4).
- GATE 2023 MA Q33 – Solve y″+4y=t for 0≤t≤2 and =2 for t>2, with y(0)=y′(0)=0. If α=y(π/2), find (4/π)α to two decimals.
- GATE 2023 MA Q41 – Let φ,ψ be independent solutions of y″+(2−cos x)y=0 on ℝ. Suppose α<β,φ(α)=φ(β)=0 and φ≠0 on (α,β). P:φ′(α)φ′(β)>0. Q:φ(x)ψ(x)≠0 throughout (α,β).…
- GATE 2023 MA Q49 – For x′=y,y′=x with x(0)=α,y(0)=β, which choices give x(t) + y(t) →0 as t→∞?
- GATE 2024 MA Q45 – A is a nondiagonalizable real 2×2 matrix with real eigenvalue λ and eigenvector v. Choose the general solution of y′=Ay, with arbitrary constants…
- GATE 2024 MA Q63 – The BVP x²y″−2xy′+2y=0 on [1,2], y(1)−y′(1)=1, y(2)−ky′(2)=4, has infinitely many solutions for which k? (two decimals)
- GATE 2025 MA Q31 – W is the real vector space of all bounded real-valued solutions on ℝ of y⁽⁴⁾+2y″+y=0. Find dim W (integer).
- GATE 2025 MA Q37 – x²y″+7xy′+9y=x⁻³ ln x for x>0, with y(1)=y′(1)=0. Find y(e).
- GATE 2025 MA Q38 – Independent solutions of (1+x²)y″−xy′+cos²x y=0 satisfy y₁(0)=3,y₁′(0)=−1,y₂(0)=−5,y₂′(0)=2. Let W=y₁y₂′−y₂y₁′. Find W(1/2).
- GATE 2026 MA Q36 – Solve y=pmatrix-3&4\\-2&3pmatrixy, y(0)=pmatrix1\\2pmatrix.