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GATE 2025 CE (CE2) – Question 29

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

The "order" of the following ordinary differential equation is ______.
$\frac{d^3y}{dx^3} + \left(\frac{d^2y}{dx^2}\right)^6 + \left(\frac{dy}{dx}\right)^4 + y = 0$

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Correct answer: 3

Explanation

The order of a differential equation is the order of the highest derivative that appears, which is the third derivative $\frac{d^3y}{dx^3}$. The powers of the other derivatives give the degree, not the order.