Question

Solve the given system of differential equation

𝑫𝒙 − 𝟐𝒙 + 𝒚 = 𝟎 , 𝑫𝒚 − 𝒙 = 0

Answer 1

$\frac{dy}{dt}=x$

$x'(t)=y''(t)$

$y'''-2y'+y=0$

$r^2-2r+1=0$

$r_{1,2}=1$

$y=c_1e^t+c_2te^t$

$x=c_1e^t+c_2e^t+c_2te^t$