Ordinary Differential Equations:Cheat Sheet/First Order Ordinary Differential Equations
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Linear, Inhomogeneous Type
[edit | edit source]General Form
[edit | edit source]
Solution
[edit | edit source], where
- is a constant and
Separable
[edit | edit source]General Form
[edit | edit source]
Solution
[edit | edit source]Rearrange to get , and integrate
Bernoulli's
[edit | edit source]General Form
[edit | edit source]
Solution
[edit | edit source]Substitute
Exact Equations
[edit | edit source]General Form
[edit | edit source], with
Solution
[edit | edit source]Solution is of the form , a constant, where and
Approximation Methods
[edit | edit source]Let
Euler's Method
[edit | edit source]Euler's method with step size is given by:
.
Improved Euler's Method
[edit | edit source]Improved Euler's method with step size is given by:
.
Runge-Kutta Method of Fourth Order
[edit | edit source]For step size ,
, where