List of top Mechanical Engineering Questions on Differential Equations asked in CUET (PG)

Which of the following are false about the differential equation: \[ (y^2 + y^3 + x^2y)\,dx + (2xy^2 - 4y^3)\,dy = 0 \] A. Linear, homogeneous and exact
B. Non-linear, homogeneous and exact
C. Non-linear, non-homogeneous and exact
D. Non-linear, non-homogeneous and inexact

Which of the following are not the solution of \( \frac{\partial^2 z}{\partial x^2} = \frac{\partial^2 z}{\partial y^2} \)? A. \(z = f(y+x) + f(y-x)\)
B. \(z = f(y+x) + f(y-x)\)
C. \(z = f(x^2 - y^2)\)
D. \(z = f(x^2 + y^2)\)

The transformed equation of \( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0 \) in polar coordinates is:

If \( \frac{d}{dx}(y) = y \sin 2x \) and \( y(0) = 1 \), then what is the required solution?

Which of the following is not a non-linear partial differential equation, where \(p = \frac{\partial z}{\partial x} \quad \text{and} \quad q = \frac{\partial z}{\partial y}?\)