DIFFERENTIAL EQUATIONS

Differential equations



Differential equations

Second Order Differential Equations

Equivalent Forms; Initial Value Problems In general, second order differential equations take the form

d2y

dx2

= f x; y;

dy

dx!

;

where f(x; y; z) is a continuous function of the variables x; y

and z in some region R and R3

and is continuously differentiable with respect to y and z throughout that region.

If we define z =

dy

dx, then we can write the above equation equivalently as a system of two (coupled) First order equations:

dy

dx = z;

dz

dx = f(x; y; z):

Written in this form and drawing on experience with First order equations, we would expect to have to give ...