Find second order linear homogeneous ODE with constant coefficients if its fundamental set of solutions is {$e^{3t},te^{3t}$}.
Attempt: Had this question in my midterm. So, since the fundamental set of solutions is $$y=y_1+y_2=c_1e^{3t}+c_2te^{3t}$$ the characteristic equation of the second order ODE has only one root. I don't know what to do next. Help please.