Maple run to compute RHS, f(w,x,y,z,t)
Given u(w,x,y,z,t) and fourth order PDE

> u(w,x,y,z,t):=t^4+2*z^4+3*y^4+4*x^4+5*w^4+6*y^2*z^2*t^2*w^2+7*w*x*y*z*t+
                8*x*z+9*t*w+10;
u(w,x,y,z,t) := t^4+2*z^4+3*y^4+4*x^4+5*w^4+6*y^2*z^2*t^2*w^2+7*w*x*y*z*t+
                8*x*z+9*t*w+10
> uw(w,x,y,z,t):=diff(u(w,x,y,z,t),w);
uw(w,x,y,z,t) := 20*w^3+12*y^2*z^2*t^2*w+7*x*y*z*t+9*t
> ux(w,x,y,z,t):=diff(u(w,x,y,z,t),x);
ux(w,x,y,z,t) := 16*x^3+7*w*y*z*t+8*z
> uy(w,x,y,z,t):=diff(u(w,x,y,z,t),y);
uy(w,x,y,z,t) := 12*y^3+12*y*z^2*t^2*w^2+7*w*x*z*t
> uz(w,x,y,z,t):=diff(u(w,x,y,z,t),z);
uz(w,x,y,z,t) := 8*z^3+12*y^2*z*t^2*w^2+7*w*x*y*t+8*x
> ut(w,x,y,z,t):=diff(u(w,x,y,z,t),t);
ut(w,x,y,z,t) := 4*t^3+12*y^2*z^2*t*w^2+7*w*x*y*z+9*w
> uww(w,x,y,z,t):=diff(uw(w,x,y,z,t),w);
uww(w,x,y,z,t) := 60*w^2+12*y^2*z^2*t^2
> uxx(w,x,y,z,t):=diff(ux(w,x,y,z,t),x);
uxx(w,x,y,z,t) := 48*x^2
> uyy(w,x,y,z,t):=diff(uy(w,x,y,z,t),y);
uyy(w,x,y,z,t) := 36*y^2+12*z^2*t^2*w^2
> uzz(w,x,y,z,t):=diff(uz(w,x,y,z,t),z);
uzz(w,x,y,z,t) := 24*z^2+12*y^2*t^2*w^2
> utt(w,x,y,z,t):=diff(ut(w,x,y,z,t),t);
utt(w,x,y,z,t) := 12*t^2+12*y^2*z^2*w^2
> uwww(w,x,y,z,t):=diff(uww(w,x,y,z,t),w);
uwww(w,x,y,z,t) := 120*w
> uxxx(w,x,y,z,t):=diff(uxx(w,x,y,z,t),x);
uxxx(w,x,y,z,t) := 96*x
> uyyy(w,x,y,z,t):=diff(uyy(w,x,y,z,t),y);
uyyy(w,x,y,z,t) := 72*y
> uzzz(w,x,y,z,t):=diff(uzz(w,x,y,z,t),z);
uzzz(w,x,y,z,t) := 48*z
> uttt(w,x,y,z,t):=diff(utt(w,x,y,z,t),t);
uttt(w,x,y,z,t) := 24*t
> uwwww(w,x,y,z,t):=diff(uwww(w,x,y,z,t),w);
uwwww(w,x,y,z,t) := 120
> uxxxx(w,x,y,z,t):=diff(uxxx(w,x,y,z,t),x);
uxxxx(w,x,y,z,t) := 96
> uyyyy(w,x,y,z,t):=diff(uyyy(w,x,y,z,t),y);
uyyyy(w,x,y,z,t) := 72
> uzzzz(w,x,y,z,t):=diff(uzzz(w,x,y,z,t),z);
uzzzz(w,x,y,z,t) := 48
> utttt(w,x,y,z,t):=diff(uttt(w,x,y,z,t),t);
utttt(w,x,y,z,t) := 24
> uwx(w,x,y,z,t):=diff(uw(w,x,y,z,t),x);
uwx(w,x,y,z,t) := 7*y*z*t
> uwxy(w,x,y,z,t):=diff(uwx(w,x,y,z,t),y);
uwxy(w,x,y,z,t) := 7*z*t
> uwxyz(w,x,y,z,t):=diff(uwxy(w,x,y,z,t),z);
uwxyz(w,x,y,z,t) := 7*t
> uwwt(w,x,y,z,t):=diff(uww(w,x,y,z,t),t);
uwwt(w,x,y,z,t) := 24*y^2*z^2*t
> uwwtt(w,x,y,z,t):=diff(uwwt(w,x,y,z,t),t);
uwwtt(w,x,y,z,t) := 24*y^2*z^2
> uxy(w,x,y,z,t):=diff(ux(w,x,y,z,t),y);
uxy(w,x,y,z,t) := 7*w*z*t
> uxyt(w,x,y,z,t):=diff(uxy(w,x,y,z,t),t);
uxyt(w,x,y,z,t) := 7*w*z
> uyyz(w,x,y,z,t):=diff(uyy(w,x,y,z,t),z);
uyyz(w,x,y,z,t) := 24*z*t^2*w^2
> uyyzz(w,x,y,z,t):=diff(uyyz(w,x,y,z,t),z);
uyyzz(w,x,y,z,t) := 24*w^2*t^2
> uztt(w,x,y,z,t):=diff(utt(w,x,y,z,t),z);
uztt(w,x,y,z,t) := 24*y^2*z*w^2
> uyyt(w,x,y,z,t):=diff(uyy(w,x,y,z,t),t);
uyyt(w,x,y,z,t) := 24*z^2*t*w^2
> uzt(w,x,y,z,t):=diff(uz(w,x,y,z,t),t);
uzt(w,x,y,z,t) := 24*y^2*z*t*w^2+7*w*x*y

PDE
> f(w,x,y,z,t):=0.5*uwwww(w,x,y,z,t)+1.5*uwxyz(w,x,y,z,t)+2.5*uwwtt(w,x,y,z,t)+
                    uxxxx(w,x,y,z,t)+  2*uyyyy(w,x,y,z,t)+  3*uzzzz(w,x,y,z,t)+
                  4*utttt(w,x,y,z,t)+  5*uxyt(w,x,y,z,t)+   6*uyyzz(w,x,y,z,t)+
                   7*uztt(w,x,y,z,t)+  8*uxxx(w,x,y,z,t)+    9*uyyt(w,x,y,z,t)+
                   10*uzt(w,x,y,z,t)+   11*ut(w,x,y,z,t)+      12*u(w,x,y,z,t);

f(w,x,y,z,t) := 216*z^2*t*w^2+60.0*y^2*z^2+768*x+168*y^2*z*w^2+35*w*z+
                144*w^2*t^2+108*t*w+96*x*z+77*w*x*y*z+99*w+10.5*t+60*w^4+
                48*x^4+36*y^4+24*z^4+12*t^4+70*w*x*y+72*y^2*z^2*t^2*w^2+
                132*y^2*z^2*t*w^2+240*y^2*z*t*w^2+44*t^3+84*w*x*y*z*t+660.0