CUET Mathematics 2025 22 May Shift 2 PYQs

The sum of order and degree of the differential equation $y = x\frac{dy}{dx} + 2\sqrt{1 + \left(\frac{dy}{dx}\right)^2}$ is

Let $e^{\alpha x} + e^{\beta x} + yx^2 + \delta \log|x| + C = 0$, where $C \in \mathbb{R}_0$ be a particular solution of the differential equation $x(e^y - 1)dy + (x^3 - 1)e^ydx = 0$ and passes through the point $(1, 1)$. The value of $(\alpha + \beta + \gamma + \delta - C)$ is

The general solution of the differential equation

$\frac{dy}{dx} = xy + x + y + 1$ is