Reducible Differential Equations

Question 1

Process where the substitution includes what you’re solving for (y with x as the other variable)

Answer 1

Rearrange the substitution for y
Find dy/dx and d^2y/dx^2
Solve as a regular first or second order DE
Substitute back for y

Question 2

d/dx(dy/du)

Answer 2

d^2y/du^2 X dy/dx

Question 3

Process where the substitution doesn’t include what you are solving for (y with substitution x = f(u))

Answer 3

Find du/dx, possibly by doing 1/(dx/du))
Using dy/dx = dy/du X du/dx find dy/dx in terms of dy/du
Differentiate again for d^2y/dx^2 and repeat if necessary
Solve for y and substitute for x