General Solution for Scalar Equation

Ex. 1: Given the differential equation is as solution?

To solve this first find the equations for and given that :

now we plug our values into the original equation:

thus is not a solution because is a false statement.

Ex. 2: Is as solution to the same differential equation?

now out differential equation looks like:

as we can see above is a solution to the differential equation because it yields a true statement.

See differential equations notes - week 1 - intro to diffeq and differential equations solution guide for more information.

How do you find a solution to a given differential equation? There are three main methods to do so:

• Integrating Factor
• Separation of Variables
• Variation of Parameters