The techniques are:

1) Reduction of Order.

2) Homogenous Linear Equation with Constant Coefficients.

3) Undetermined coefficients; Superposition Approach.

4) Undetermined coefficients; Annihilator Approach.

5) Variation of Parameters.

6) Cauchy-Euler Equation.

7) Solving Systems of Linear Differential Equations by Elimination.

Search an interesting physical model which can be represented as an ordinary differential equation. Explain it's working in detail and estimate exact solution by the listed techniques