The general solution of the differential equation $\frac{dy}{dx} = \cos(x+y)$ is

If the slope of the tangent at a point $(x, y)$ on a curve is $\frac{y-4}{x-3}$ and the curve passes through $(4, 3)$,then the point where it cuts the line $y=x$ is

Let a smooth curve $y=f(x)$ be such that the slope of the tangent at any point $(x, y)$ on it is directly proportional to $\left(\frac{-y}{x}\right)$. If the curve passes through the points $(1, 2)$ and $(8, 1)$,then $\left| y \left(\frac{1}{8}\right) \right|$ is equal to

$A$ particle moves in a straight line with a velocity given by $\frac{dx}{dt} = x + 1$ (where $x$ is the distance covered). The time taken by the particle to traverse a distance of $99 \ m$ is:

The equation of the curve passing through the point $(0, -2)$ given that at any point $(x, y)$ on the curve,the product of the slope of its tangent and the $y$-coordinate of the point is equal to the $x$-coordinate of the point,is

If $x^{3} dy + xy dx = x^{2} dy + 2y dx$,$y(2) = e$ and $x > 1$,then $y(4)$ is equal to