systemDE.sagews

t = var('t')
sage: x = function('x')(t)
sage: y = function('y')(t)
sage: de1 = diff(x,t)  == 3*x+y
sage: de2 = diff(y,t) == 2*x+2*y
sage: ss=desolve_system([de1, de2], [x,y], ics=[0,1,0])
show(ss)

[$\displaystyle x\left(t\right) = \frac{2}{3} \, e^{\left(4 \, t\right)} + \frac{1}{3} \, e^{t}$, $\displaystyle y\left(t\right) = \frac{2}{3} \, e^{\left(4 \, t\right)} - \frac{2}{3} \, e^{t}$]