The differential equation $\frac{dy}{dx} = \frac{1}{ax + by + c}$,where $a, b, c$ are all non-zero real numbers,is

Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}=\frac{(\tan x)+y}{\sin x(\sec x-\sin x \tan x)}$,$x \in\left(0, \frac{\pi}{2}\right)$ satisfying the condition $y\left(\frac{\pi}{4}\right)=2$. Then,$y\left(\frac{\pi}{3}\right)$ is

If $u(x)$ and $v(x)$ are two independent solutions of the differential equation $\frac{d^{2} y}{d x^{2}}+b \frac{d y}{d x}+c y=0$, then which of the following is also a solution of the given differential equation?

Let $y(x)$ be the solution of the differential equation $2 x^{2} dy + (e^{y} - 2x) dx = 0$,$x > 0$. If $y(e) = 1$,then $y(1)$ is equal to:

The general solution of the differential equation $\frac{dy}{dx} + xy = 4x - 2y + 8$ is

The equation of the curve passing through the point $(0, 1)$ and having a slope of the tangent at any point $(x, y)$ equal to $\frac{y}{x + y}$ is: