If u(t) = 1, then your solution is right.
If it is a function with respect to time, then your solution is wrong.
Exact code:
syms y(t) u(t) t
dy = diff(y,t,1);
d2y = diff(y,t,2);
eq = d2y + 12*dy + 32*y - 32*u;
conds = [y(0)==0; dy(0) ==0];
dsolve(eq, conds)
