Converting a Third-Order Differential Equation into a Vector System?

[johnaphun]

Homework Statement

Convert the differential equation for x,

x''' + 2(x''²) = 0

Into a system of first order differential equations. Put the system in vector form

Homework Equations

The Attempt at a Solution

I'm able to do this for simpler DE's but I can't seem to find an answer for this one. Do i need to do anything different because of the 3rd derivative?

 

[tiny-tim]

hi johnaphun!

what's the difficulty?

put a = x'' and solve, then put v = x' and solve

 

[HallsofIvy]

Same thing except that I tend to prefer to use letters near the beginning of the alphabet, like "a", to represent constants, letters near the end, like "x", to represent variables.

Since your equation is x'''+ 2(x'')^2= 0, let y= x' and z= y'= x'' so that x'''= z'. Now, x'''+ 2(x'')^2= z'+ 2z^2= 0, y'= z, and x'= y.

 

[tiny-tim]

Same thing except that I tend to prefer to use letters near the beginning of the alphabet, like "a", to represent constants, letters near the end, like "x", to represent variables.

Normally, I'd agree! … but this equation looked to me like a dynamical equation, with x being distance, so I preferred the familiar form of x' = v, v' = a.