I need to know how to do the following for which I am allowed to get help, but no one knows how to help me:
Find a linear differential equation with constant real coefficients for which y1(t)=(t^2)(e^t) and y2(t)= (tsint) are two solutions.
And another similiar problem is:
Given that y1(t)= 1, y2(t)= t, y3(t)=t^(-2) are solutions of the homogeneous eqution y''' +(4t^-1)y''=0, find the general solution of the differential equation y'''+(4t^-1)y''=g(t). [the coefficient of y'' is 4t to the negative one power or 4/t]