Examples of differential equations: Difference between revisions

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== Separable first-order ordinary differential equations ==

{{see also|Separable partial differential equation}}

Equations in the form <math>\frac {dy}{dx} = f(x)g(y)</math> are called separable and solved by <math>\frac {dy}{g(y)} = f(x)\,dx</math> and thus

<math>\int\frac {dy}{g(y)} = \int f(x)\,dx</math>. Prior to dividing by <math>g(y)</math>, one needs to check if there are stationary (also called equilibrium)

solutions <math>y=const\text{constant}</math> satisfying <math>g(y)=0</math>.

==Separable (homogeneous) first-order linear ordinary differential equations==