The Laplace transform of
Obtaining Differential Equations from Functions
is a first order ODE,
is a second order ODE and so on. I am having trouble to obtain a differential equation from a given function. I could find the differential equation for
using the orginal function and (1). Finally,
which is the required differential equation.
Similarly, if the function is
following similar steps as above.
Transform the given initial value problem into an initial value problem for two first-order quations