Differential Equations

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First Order DE

Homogeneous first order differential equation:



General solution:




Non-homogeneous first order differential equation:



General solution:

, where A(t) is the primitive function of a(t).


Second Order DE

Homogeneous second order differential equation:



General method of solution:

Substitution: gives ,

which is a first order differential equation.



Non-homogeneous second order differential equation:



General method of solution:

Let be a particular solution of the homogeneous equation
. Then the substitution gives

gives , which is a
homogenous second order differential equation.

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