# Thread: Writing first order vector diffferential equations

1. ## Writing first order vector diffferential equations

Hi all,

I have the question: write the following system of third-order scalar homogeneous differential equations as a first-order vector differential equation of the form x'(t)=Ax(t):

y'''+2y'+y-3z'+z=0
2z'''+z'''-4y''+2z+6y=0

I want to create a column vector x(t) which uses the variables y and z and includes all the derivatives up to one less order than the ODE i.e x(t) should include y,y',y'' and z,z',z''. I'm not sure exactly how to write this, could someone start me off please. Any help is appreciated

Thank you

2. ## Re: Writing first order vector diffferential equations

To start you off, how about $x_{1}=y,\;x_{2}=y'\;x_{3}=y'',\dots?$