Do you need to solve a differential equation?

Is it homogenous?

If not, you will need the particular solution added to the homogenous solution.

To get the homogenous solution, follow this video

To get the particular solution, you'll need to identify the driving force. What type of function is the driving force?

If it is a polynomial, follow this video. Remember to add it on to the homogenous solution. At^2 + Bt + C

If it's a trigonometric function, follow this video. (Acost + Bsint)

If it's an exponential function, follow this video. Ae^t

If it's a combination of any of these, follow this video (multiply them together)

If yes, does it involve complex roots?

If not, follow this video. (Homogenous with real roots)

If it involves complex roots, follow this video. (Homogenous with imaginary roots)

use the eigenvalues/eigenvectors method

Is the DE separable?

If yes, solve by using Separation of Variables
(click play for video tutorial)

If not, use the Integrating Factor Method
(click play for video tutorial)