This equation is in the form:
dydT=A(T)y+B(T)\frac{dy}{dT} = A(T) \cdot y + B(T)
The solution in general:
y(T)=eA(T)dT[B(T)eA(T)dTdT+C]y(T) = e^{\int A(T)\,dT} \left[ \int B(T) \cdot e^{-\int A(T)\,dT} \,dT + C \right]
Then the solution to G~i(Ta)\widetilde{\mathcal{G}}_i(T_a) is:
G~i(Ta)=eAi(Ta)dTa[Bi(Ta)eAi(Ta)dTadTa+Ci]\widetilde{\mathcal{G}}_i(T_a) = e^{\int A_i(T_a)\,dT_a} \left[ \int B_i(T_a) \cdot e^{-\int A_i(T_a)\,dT_a} \,dT_a + C_i \right]
Physical Interpretation
First termeAie^{\int A_i} denotes the exponential effect of resonance between the fundamental forces.
Second integral term shows the contribution from the absolute time resonance field R(Ta)\mathcal{R}(T_a).
Konstanta CiC_iis the initial value of the fundamental force at time T0T_0, which can be determined from the initial conditions (e.g. from the initial cosmological conditions).
8. Empirical and Existential Implications
