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GATE 2026 EE – Question 14

Engineering Mathematics · Differential Equations: First order equations, Higher order linear differential equations, Variation of parameters, Cauchy and Euler equations, Partial differential equations, Separation of variables · 1 mark · Multiple choice

Consider the following differential equation:

$$t^2\frac{d^2y}{dt^2}+7t\frac{dy}{dt}+8ty=10\sin(t)$$

Which one of the following options is correct?

  1. It is a linear differential equation
  2. It is a nonlinear differential equation
  3. It is a time-invariant differential equation
  4. It is a second-order partial differential equation

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Correct answer: (A) It is a linear differential equation

Explanation

$y$ and its derivatives appear only to the first power and are not multiplied together, so the equation is linear. The coefficients $t^2$, $7t$ and $8t$ depend on $t$, so it is time-varying (not time-invariant). It involves only one independent variable, so it is an ordinary (not partial) differential equation.