The area of the region ( in sq units) enclosed by the curve $y=x^3-19 x+30$ and the $X$-axis, is

The differential equation representing the family of circles having their centres of Y -axis is $\left(y_1=\frac{d y}{d x}\right.$ and $\left.y_2=\frac{d^2 y}{d x^2}\right)$

The general solution of the differential equation $\left(\sin y \cos ^2 y-x \sec ^2 y\right) d y=(\tan y) d r$, is

The general solution of the differential equation $(x-y-1) d y=(x+y+1) d x$ is