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## Main Question or Discussion Point

My question is in regards to converting a system of differential equations into a higher order differential equation. I am an undergrad taking diff eq and have just learned the wonders of Euler's method of solving 2nd order differential equations with constant coefficients. It is significantly faster then using eigenvalues and eigenvectors.

My question is:

Can I always convert a system of (2) 1st order differential equations into (1) 2nd order differential equation?

If not, what attributes of the system allow me to identify that it cannot be converted?

Can I always convert a system of n-order differential equations into a single n-order differential equation? (I do not know why I would want to do this since Euler's method would not help in this instance, but you may as well generalize your answer if possible.)

Thank you in advance for any feedback.

Bizoid

My question is:

Can I always convert a system of (2) 1st order differential equations into (1) 2nd order differential equation?

If not, what attributes of the system allow me to identify that it cannot be converted?

Can I always convert a system of n-order differential equations into a single n-order differential equation? (I do not know why I would want to do this since Euler's method would not help in this instance, but you may as well generalize your answer if possible.)

Thank you in advance for any feedback.

Bizoid