Question

Express the 4th-Order differential equation as a system of first order differential equations using matrix notation

Answer 1

\[y^{(4)}+\frac{ y^{(3)} }{ t^{2} }+\sin(ty'')+e^ty=t^2\]

Answer 2

i know to do this, we need to set the derivative of y to another variable, but i'm confused on the steps to do so, and how that will actually help solve this too

Answer 3

do i just set something like:

\[y^{(3)} = x_1 \]
and\[y^{(4)} = x_1'\]