Solve ${\displaystyle \frac{dy}{dx}}=2x+4$ given that $P(2,-1)$ lies on the curve

The adjacent graph is the direction field of a first order differential equation. The differential equation could be: 

Given the differential equation ${\displaystyle \frac{dy}{dx}}-y+x=0$ and given that the solution curve passes through the point $(2,-1)$, then the gradient of the solution curve is?

The particular solution to ${\displaystyle \frac{dy}{dx}}=x(x^2-4{)}^3$, given that $y=1$ and $x=2$

Find the general solution to $y^{\prime }=2{\sin }^{2}x$

Find the particular solution to ${\displaystyle \frac{dy}{dx}}={\sin }^{2}y$, given that $x=0$ and $y={\displaystyle \frac{\pi }{2}}$

Find the general solution to $y^{\prime }=1+y$

Find the particular solution to $(1-x^2){\displaystyle \frac{dy}{dx}}=xy$, given that $x=0,y=1$

Find the general solution to $\sec x{\displaystyle \frac{dy}{dx}}-y^2=0$

For a body falling under gravity, the rate of change of velocity is given by ${\displaystyle \frac{dv}{dt}}=-0.02(v-490)$. Find the velocity after 5 seconds, given that when $t=0,v=0$. 

The rate of cooling of a metal object, initially at $T={125}^{\circ }C$, is given by ${\displaystyle \frac{dT}{dt}}=-0.64(T-30)$, where $t$ is in hours. Find how long it would take for the object to cool to ${66}^{\circ }C$