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A linear second order differential equation involves a function, and it's first and second derivative. It can be written as 

$ {A(x)y''+B(x)y'+C(x)y = D(x)} $

One important note: Linear combinations of solutions to a linear homogeneous differential equations are also solutions.


Linear

Homogeneous equations

Reducible
Characteristic Equation

Non-homogeneous equations

Undetermined Coefficients
Variation of Parameters

Systems of Equations

Elimination

Eigenvalue