A differential equation is any equation with one or more differential terms –
or similar.
Given
to find
we differentiate
To find
we differentiate
We can differentiate any number of times: if we differentiate y n times, we have
Examples of differential equations include:
If a function
is a solution to the differential equation then we can substitutefor
into the equation and obtain an identity.
Example: Show that
satisfies the equation
Hence the given function satisfies the equation.
Example: Show that
satisfies the equation
Hence the given function satisfies the equation.