Consider two Ordinary Differential Equations (ODEs): P: $ \dfrac{dy}{dx} = \dfrac{x^4 + 3x^2 y^2 + 2y^4}{x^3 y} $ Q: $ \dfrac{dy}{dx} = -\dfrac{y^2}{x^2} $ Which one of the following options is CORRECT?

P is a homogeneous ODE and Q is not an exact ODE.

P is a homogeneous ODE and Q is an exact ODE.

P is a homogeneous ODE and Q is not an exact ODE.

P is a nonhomogeneous ODE and Q is an exact ODE.

P is a nonhomogeneous ODE and Q is not an exact ODE.

GATE 2024 Civil Engineering PYQ — Engineering Mathematics

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Engineering Mathematics · Differential Equations (CE)

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Differential Equations (CE) has appeared in GATE Civil Engineering 63 times across 26 years (2017, 2022, 2023, 2024, 2025, ...).

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ordinary differential equationshomogeneous odeexact ode