11 - Introduction to Reducible Second Order ODEs
What are these "reducible second order ordinary differential equations"?
Like we said, since derivatives have orders, so do differential equations.
In the context of differential equations, this order is the highest order derivative present in the equation.
This means that we can make a substitution. Some kind of variable that represents the first derivative. When we have this, we can represent the second derivative as the first derivative of this variable.
Effectively, we are "reducing" this differential equation to a first order one.
There will be two cases when doing this type of solving. Either the variable x, or the variable y will be gone. We'll get into that in a bit.
Since we have a second order ODE, we'll be "undoing" two differentiations. This means that we'll end up with two constants