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GATE 2026 BT – Question 27

Engineering Mathematics · Differential Equations: First order ODEs, higher order ODEs with constant coefficients, Cauchy and Euler equations, Laplace transforms · 1 mark · Multiple select

The equation $\frac{d^2y}{dx^2} - y = 0$ has a solution of the form $y = e^{Ax}$. The value(s) of A satisfying this is/are:

  1. 0
  2. 1
  3. -1
  4. $-\infty$

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Correct answer: (B) 1; (C) -1

Explanation

Substituting $y = e^{Ax}$ gives $A^2e^{Ax} - e^{Ax} = 0$, so $A^2 = 1$ and $A = \pm 1$.