Second-Order Homogeneous Equations (Constant Coefficients Introduction)

This ordinary differential equations video gives an introduction to second-order homogeneous linear equations with constant coefficients, and explains the characteristic polynomial (also called the auxiliary equation) and shows how to use the solution for this quadratic equation to solve the differential equation. We show how exponential functions make up the fundamental solution set and how to find the solutions. We also describe the three possibilities for the solutions to the characteristic polynomial: distinct real roots, repeated real roots, and complex conjugate roots.
0:00 What do these look like?
0:41 Characteristic Polynomials
3:57 Example
5:47 3 Polynomial Solution Possibilities

[feralfalafel]

So what would the solution look like for case 2 for the values of m? Would it be y = c1e^mx or y = c1e^mx + c2e^mx?
Thanks