A second order linear homogeneous ordinary differential equation with constant coefficients can be expressed as
This equation implies that the solution is a function whose derivatives keep the same form as the function itself and do not explicitly contain the independent variable , since constant coefficients are not capable of correcting any irregular formats or extra variables. An elementary function which satisfies this restriction is the exponential function .
Substitute the exponential function into the above differential equation, the characteristic equation of this differential equation is obtained
This characteristic equation has two roots and .
2nd Order Linear Homogeneous ODE with Constant Coefficients:

Characteristic Equation: 
Solutions of Characteristic Equation , 
General Solution 
1 


2 


3 


