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GATE 2014 EC (EC3) – Question 12

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

Which is a linear nonhomogeneous differential equation, with independent variable x and dependent variable y?

  1. $dy/dx+xy=e^{-x}$
  2. $dy/dx+xy=0$
  3. $dy/dx+xy=e^{-y}$
  4. $dy/dx+e^{-y}=0$

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Correct answer: (A) $dy/dx+xy=e^{-x}$

Explanation

A linear first-order equation has form y′+p(x)y=q(x), where q is a function of the independent variable only. A is y′+xy=e⁻ˣ with nonzero forcing, so **A** qualifies. B is homogeneous; C and D contain e⁻ʸ and are nonlinear in the dependent variable.