Transform the given equation into a system of first order eq

Transform the given equation into a system of first order equations. (Let x1 = u and x2 = u\'. Enter your answers in terms of x1 and x2.)

u\'\' + 0.5u\' + 6u = 9 sin t

Solution

x2=u\'=x1\'

x2=x1\'

u\'\'+0.5u\'+6u=9 sin(t)

(u\')\'+0.5x2+6x1=9 sin(t)

x2\'=-0.5x2-6x1+9 sin(t)