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GATE 2026 ME – Question 13

Engineering Mathematics · Differential Equations: First order and higher order linear equations, Euler-Cauchy equation · 1 mark · Multiple choice

The order and degree of the following differential equation are $m$ and $n$, respectively.

$$\frac{\partial^3\varphi}{\partial x^3} + \frac{\partial^2\varphi}{\partial y^2}\frac{\partial\varphi}{\partial x} + \left(\frac{\partial^2\varphi}{\partial x^2}\right)^2 + \frac{\partial\varphi}{\partial y} = 0$$

The value of $(m - n)$ is

  1. 2
  2. 3
  3. 1
  4. 0

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Show answer and explanation

Correct answer: (A) 2

Explanation

The highest derivative is $\frac{\partial^3\varphi}{\partial x^3}$, so the order is $m = 3$. The degree is the power of that highest-order derivative, which is 1, so $n = 1$. The squared term has a lower order and does not count. So $m - n = 2$.