Linear Differential Equations

Linear differential equations and some special quasi-linear differential equations which can be linearized are listed in the following table. Their solutions or simplifying methods are also presented.

Differential Equation General Solution/Simplifying Method
Linear differential equation:

where is the integrating factor.
Bernoulli's differential equation:

which is a linear differential equation.
Ricatti's differential equation:

which is the Bernoulli's differential equation with n=2 and a non-homogeneous term .

where is the particular solution.