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GATE 2025 AG – Question 14

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

Classify $y^{\prime\prime}+p(x)y^{\prime}+q(x)y=r(x)$.

  1. Second order, nonhomogeneous and linear
  2. Second order, homogeneous and linear
  3. Second order, homogeneous and nonlinear
  4. First order, nonhomogeneous and linear

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Correct answer: (A) Second order, nonhomogeneous and linear

Explanation

The highest derivative is second order. The dependent variable and its derivatives occur only to first power and are not multiplied together, so the ODE is linear. With a general nonzero forcing $r(x)$ it is nonhomogeneous: **A**. If $r$ were identically zero, the homogeneous special case would instead apply.

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