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GATE 2022 BT – Question 11

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

What is the order of the differential equation $d^2y/dx^2-6x=3x^4-2x^3+2$?

  1. 1
  2. 2
  3. 3
  4. 4

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Correct answer: (B) 2

Explanation

The **order** of a differential equation is the order of the highest derivative that appears in it.

The equation is
$$\frac{d^2y}{dx^2}-6x=3x^4-2x^3+2 .$$

The highest derivative is $\dfrac{d^2y}{dx^2}$, the second derivative. The polynomial terms in $x$ do not affect the order.

The order is **2** (option B).