Given the ODE
$x'''(t)=t^2\sin(x'')+\cos(x)+1$,
i've got to convert it into a system of first order.
My first try is:
$z_0=x \\ z_1=x'\\ z_2=x''$
then I get:
$z_0'=x'=z_1 \\ z_1'=x''=z_2 \\ z_2'=x'''=t^2\sin(z_2)+\cos(z_0)+1$,
but I can't transform it into a matrix with constant coefficient. I want to transform it in order to find a solution of this ODE. Or is there another way?