Question

My professor showed us in class today how to use ode45 to solve a differential equation numerically. i would like to use it on my homework but i have a second order differential equation and the example i saw in class was only first order. can ode45 be used for second order diffeqs? what do i need to do differently? the equation i am trying to solve is:

Answer 1

Yes, ode45 can be used for higher-order differential equations. You need to convert the higher order equation to a system of first-order equations, then use ode45 on that system.

For example, if you have

... u'' + a·u' + b·u = f

you can define u1 = u, u2 = u' and now you have the system

... (u2)' + a·u2 + b·u1 = f

... (u1)' = u2

Rearranging, this is

... (u1)' = u2

... (u2)' = f - a·u2 - b·u1

ode45 is used to solve each of these. Now, you have a vector (u1, u2) instead of a scalar variable (u). A web search regarding using ode45 on higher-order differential equations can provide additional illumination, including specific examples.