If the curve $y = y(x)$ represented by the solution of the differential equation $(2xy^2 - y)dx + xdy = 0$ passes through the intersection of the lines $2x - 3y = 1$ and $3x + 2y = 8$,then $|y(1)|$ is equal to ...... .

The solution of the differential equation $\frac{d^2 y}{d x^2}+y=0$ is

The foci of the curve which satisfies the differential equation $(1 + y^2) dx - xy\, dy = 0$ and passes through the point $(1, 0)$ are:

The solution of $\frac{d^2y}{dx^2} = \cos x - \sin x$ is

The solution of $(1+xy)y \, dx + (1-xy)x \, dy = 0$ is:

Statement $-1$: The slope of the tangent at any point $P$ on a parabola,whose axis is the $x$-axis and vertex is at the origin,is inversely proportional to the ordinate of the point $P$.
Statement $-2$: The system of parabolas $y^2 = 4ax$ satisfies a differential equation of degree $1$ and order $1$.