# filename = ode4mpl
# differential equation:
#  z4 + E3*z3 + E2*z2 + E1*z1 + E0*z0=0,
# where $a_1=a_2=a_3=p$

E0:= -(3/4)*(6*t^5*a0^2+12*a0*t^5+6*t^5-3*p*t^5+36*t^4*a0^2+70*a0*t^4+30*t^4-3*p*t^4+72*t^3*a0^2+188*a0*t^3+162*t^3+15*p*t^3+48*a0^2*t^2+246*t^2*a0+246*t^2+3*p*t^2+116*a0*t+168*t-24*p*t+16*a0+36+12*p)*p/((2*t+1)^2*(t+2)^2*(t+1)^2*(t-1)^3):

E1:= -(22*p+20*a0+140*t^3*a0^2+84*a0*t-3*t^5*a0^2+47*t^4*a0^2+114*a0^2*t^2+33*a0*t^4-3*a0*t^5-a0*t^6+120*t^2*a0+71*a0*t^3-2*a0^2*t^6+18*t^5*a0^3+36*a0^3*t^4+3*a0^3*t^6+28*a0^2*t+24*a0^3*t^3+111*p*t+60*p*t^2-75*p*t^4-89*p*t^3-24*p*t^5-5*t^6*p+96*p*t^2*a0+15*p*t^3*a0-87*p*t^4*a0-69*p*t^5*a0-15*t^6*p*a0+60*p*t*a0)/((2*t+1)^2*(t+2)^2*(t+1)^2*(t-1)^3):

E2:= (10+20*p+22*t+16*a0+136*t^3*a0^2+126*a0*t-40*t^3-23*t^2+67*t^5*a0^2+147*t^4*a0^2+44*a0^2*t^2-45*a0*t^4-69*a0*t^5-14*a0*t^6+285*t^2*a0+187*a0*t^3+11*a0^2*t^6+3*t^6+14*t^5+14*t^4+72*p*t+69*p*t^2-81*p*t^4-19*p*t^3-51*p*t^5-10*t^6*p)/((t-1)^2*(2*t+1)^2*(t+2)^2*(t+1)^2):

E3:= -2*(3*a0*t^3-3*t^3+9*t^2*a0-7*t^2+6*a0*t+5*t+5)/((t-1)*(2*t+1)*(t+2)*(t+1)):