Introduction to 2nd order, linear, homogeneous differential equations with constant coefficients.
Linear differential equations that contain second derivatives
Another example where the nonhomogeneous part is a polynomial
What happens when the characteristic equation has complex roots?
Using the method of undetermined coefficients to solve nonhomogeneous linear differential equations.
Lets do an example with initial conditions!
What happens when the characteristic equations has complex roots?!
Another example with initial conditions!
Another example using undetermined coefficients.
What happens when the characteristic equation only has 1 repeated root?
Let's use some initial conditions to solve for the particular solution
An example where we use initial conditions to solve a repeated-roots differential equation.
Putting it all together!
Now that we've made the equation exact, let's solve it!
Differential equations with only first derivatives.
Description: Translation of: A treatise on differential equations
First example of solving an exact differential equation.
Supplemental catalog subcollection information: American Libraries Collection; Johns Hopkins University Dissertations; Thesis (Ph. D.)--Johns Hopkins University, 1887; Will digitize
Some more exact equation examples
Thesis (Ph. D.)--Johns Hopkins University, 1887
Chain rule using partial derivatives (not a proof; more intuition).
Another separable differential equation example.