GATE AG 2020 • Q13 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Higher order linear ODEs with constant coefficients

Question Statement:

Find the general solution to $\frac{d^3y}{dx^3} - 6\frac{d^2y}{dx^2} + 11\frac{dy}{dx} - 6y = 0$:

Options:

  • (A) C₁e⁻ˣ+C₂e⁻²ˣ+C₃e⁻³ˣ
  • (B) C₁e⁻ˣ+C₂e⁻²ˣ+C₃e³ˣ
  • (C) C₁e⁻ˣ+C₂e²ˣ+C₃e³ˣ
  • (D) C₁eˣ+C₂e²ˣ+C₃e³ˣ

Official Answer Key:

D

Step-by-Step Solution & Explanation

Auxiliary/characteristic equation: r³−6r²+11r−6=0 ⇒ (r−1)(r−2)(r−3)=0 ⇒ r=1,2,3. General solution: y = C₁eˣ+C₂e²ˣ+C₃e³ˣ.

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