Solve differential equation y=e^(6x)−3x−2

${\displaystyle \dot{x}=rx-h{x}^2+q}$, where ${\displaystyle \dot{x}=\frac{dx}{dt}}$. I'm assuming ${\displaystyle r,h,q}$ have different units.
I first tried ${\displaystyle \tau =\frac{t}{t_0}}$ and ${\displaystyle A=\frac{x}{x_0}}$. Then I got ${\displaystyle \frac{dA{x}_0}{d\tau t_0}=rA{x}_0-h{A}^2{x}_0^2+q}$. But I am not really sure where to go from there.
Need any help.

How is ${\displaystyle y^{\prime }\left(x\right)=f(x,y\left(x\right))}$ is the most general first order ordinary differential equation ? Isn't ${\displaystyle f(x,y\left(x\right),y^{\prime }\left(x\right))=0}$ the most general first order ODE ? I mean isn't a restriction to single out ${\displaystyle y^{\prime }\left(x\right)}$ from ${\displaystyle f}$? Thank you for your help!

Solve the differential equation $(x-3y)dx-xdy=0$

I am curious if there are any examples of functions that are solutions to second order differential equations, that also parametrize an algebraic curve.
I am aware that the Weierstrass $\mathrm{\wp }$ - Elliptic function satisfies a differential equation. We can then interpret this Differential Equation as an algebraic equation, with solutions found on elliptic curves. However this differential equations is of the first order.
So, are there periodic function(s) $F(x)$ that satisfy a second order differential equation, such that we can say these parametrize an algebraic curve?
Could a Bessel function be one such solution?

Evaluate the indefinite integral as an infinite series. ${\displaystyle \int \frac{\cos x-1}{x}dx}$

Solve differential equation$x{y}^{\prime }+2y=-x^3+x,y(1)=2$

Is a first order differential equation categorized by $f(y^{\prime },y,x)=0$ or $y^{\prime }=f(y,x)$?
In the case of the second, why $\sin y^{\prime }+3y+x+5=0$ isnt a first order differential equation?