List of top Differential Equations Questions asked in IIT JAM MA

An integrating factor of the differential equation
\[ \left( y + \frac{1}{3} y^3 + \frac{1}{2} x^2 \right) \, dx + \frac{1}{4} (x + x^2)^2 \, dy = 0 \] is

In \( \mathbb{R}^2 \), the family of trajectories orthogonal to the family of asteroids \( x^{2/3} + y^{2/3} = a^{2/3} \) is given by