nA -> products n=integer → dCA(t)/dt =-k*CA(t)**n ........................................................... depending on n: n=1,mono,n=2,bi,n=3,tri molecular reaction k =reaction rate constant CA = Concentation of A as function of time :CA(t) ........................................................... Eq(CA(t), Piecewise(((-C1*n + C1 + k*n*t - k*t)**(-1/(n - 1)), Ne(n, 1)), (nan, True))) Eq(CA(t), Piecewise((C1*exp(-k*t), Eq(n, 1)), (nan, True))) n=integer, dCA(t)/dt =-k*CA(t)**1 .................................. Eq(CA(t), CA0*exp(-k*t)) n≠1, dCA(t)/dt =-k*CA(t)**n ,n=2 .................................. 1/(k*t + 1/CA0) n≠1, dCA(t)/dt =-k*CA(t)**n ,n≠1 ................................. Piecewise(((-C1*n + C1 + k*n*t - k*t)**(-1/(n - 1)), Ne(n, 1)), (nan, True)) list of symbols = [t, k, n, C1] ........................................................................... .................... analysis : Piecewise .................... Piecewise(((-C1*n + C1 + k*n*t - k*t)**(-1/(n - 1)), Ne(n, 1)), (nan, True)) ........................................................................... ((-C1*n + C1 + k*n*t - k*t)**(-1/(n - 1)), Ne(n, 1)) (-C1*n + C1 + k*n*t - k*t)**(-1/(n - 1)) .................... find : C1,solve .................... eq = Eq((-C1*n + C1 + k*n*t - k*t)**(-1/(n - 1)), CA(t)) eq1 = Eq((-C1*n + C1)**(-1/(n - 1)), CA(0)) eq2 = Eq(C1, -(1/CA(0))**(n - 1)/(n - 1)) eq3 = Eq((k*n*t - k*t + n*(1/CA(0))**(n - 1)/(n - 1) - (1/CA(0))**(n - 1)/(n - 1))**(-1/(n - 1)), CA(t)) eq4 = Eq(CA(t), ((k*t*(n - 1)**2 + n*(1/CA(0))**(n - 1) - (1/CA(0))**(n - 1))/(n - 1))**(-1/(n - 1))) check :solt = [Eq(CA(t), Piecewise(((-C1*n + C1 + k*n*t - k*t)**(-1/(n - 1)), Ne(n, 1)), (nan, True))), Eq(CA(t), Piecewise((C1*exp(-k*t), Eq(n, 1)), (nan, True)))] check ,n=2,reason see above eq5 = False check ,n=1,reason see above eq6 = False