Transform the given equation into a system of first order eq

Transform the given equation into a system of first order equations. u\" + 8.5 u\' + 9u = 3 sin (t) Use variables X_1 and X_2 to express the given equation into a system of first order equations.) X_1\' = x_2 X_2 =

Solution

We can write higher order differential equations as a system with a very simple change of variable. We’ll start by defining the following two new functions.

x₁ = u ==> x\'₁ = u\' = x₂

x₂ = u\' ==> x₂\' +8.5x₂ +9x₁ = 3sin(t)