Imaginary Roots Differential Equations. And i think light blue is a suitable color for that. The example below.
Second order linear homogeneous des with constant coe cients. The damped oscillator 3. Then we look at the roots of the characteristic equation.
We will now explain how to handle these differential equations when the roots are complex.
In this section we discuss the solution to homogeneous linear second order differential equations ay by c 0 in which the roots of the characteristic polynomial ar 2 br c 0 are complex roots. The example below demonstrates the method. We have already addressed how to solve a second order linear homogeneous differential equation with constant coefficients where the roots of the characteristic equation are real and distinct. So in that situation let me write this the complex roots this is a complex roots scenario then the roots of the characteristic equation are going to be i don t know some number let s call it lambda.