List of top Mathematics Questions on Differential equations asked in AIEEE

The general solution of the differential equation $\frac{dy}{dx}+\frac{2}{x}y=x^{2}$ is

Let $I$ be the purchase value of an equipment and $V(t)$ be the value after it has been used for $t$ years. The value $V(t)$ depreciates at a rate given by differential equation $\frac{d V(t)}{d t}=-k(T-t),$ where $k>0$ is a constant and $T$ is the total life in years of the equipment. Then the scrap value $V(T)$ of the equipment is

Consider the differential equation $y^{2}dx +\left(x-\frac{1}{y}\right) dy = 0$. If $y \left(1\right) = 1$, then x is given by :

The curve that passes through the point (2, 3), and has the property that the segment of any tangent to it lying between the coordinate axes is bisected by the point of contact is given by :

Solution of the differential equation $cos\, x\, dy = y(sin\, x - y) dx,\, 0 < x < \frac{\pi}{2}$ is

The differential equation which represents the family of curves $y=c_1e^{c_2x}$, where $c_1$ and $c_2$ are arbitrary constants is