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GATE 2020 CE (CE2) – Question 11

Engineering Mathematics · ODE: First order and higher order linear equations, Euler-Cauchy equations, initial and boundary value problems · 1 mark · Multiple choice

Classify $d^2u/dx^2-2x^2u+\sin x=0$.

  1. Linear and homogeneous
  2. Linear and nonhomogeneous
  3. Nonlinear and homogeneous
  4. Nonlinear and nonhomogeneous

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Show answer and explanation

Correct answer: (B) Linear and nonhomogeneous

Explanation

The unknownu and its derivatives occur only to the first power,with coefficients depending onx,so the ODE is linear. Moving sinx to the right gives a nonzero forcing−sinx,so it is nonhomogeneous. **Answer:B**.