Solving 4th Differential Equation

Hello. I have an assignment to do and the assignment including ( Solve This Differential Equation using Matlab ), and the DE is:

I tried to solve it using 'dsolve' code but I had some problems, the output is very long terms ( are this normal thing?) , and the output appeared as a function of x (matlab didn't sub. by x in dsolve), I used this code to solve:

u = inline ('(t>=0)' , 't');
syms t;
x = 5*sin(300*pi*t)*u(t) + 3*u(t);
xdiff = diff(x,t);
y = dsolve('D4y+3*D3y-D2y+Dy-7*y=3*xdiff + 5*x' , 'y(0)=0' , 'Dy(0)=0' , 'D2y(0)=0' , 'D3y(0)=-5' , 't' );

So please tell me what the error here?? or maybe 'dsolve' can't solve 4th order DE? if yes please tell me how I can solve it.

Thank you ..