I must approximate the coefficients a, b, c, and d in an exponential equation. Is it possible to plot?

Please help!

Ea := 0.00762014687*t + a*t^2 + b*t^3 + c*t^4 + d*t^5;
E1 := diff(Ea, t);
E2 := subs(t = 435, Ea);
E3 := subs(t = 528, Ea);
E4 := subs(t = 33168, Ea);

E1 = 5.012764943*10^(-24)*Ea/(exp(Ea/(4.100527530*10^(-21))) - 1)

Aph1.mw

I have the function  and derivate with respect to ν and make the change variable ν=1/t it seems it doesn’t work. I put the derivate of 1/t => -1/t² by hand  (could it be done by “dchange” the hole transformation ?)

I want to approximate the value of the integral. It seems that the solution of the equation and plot in 2 situations for low-frequency ν < 10¹⁴  and for high frequency so  when the exponential is dominated.

Thus plot the whole function E2 in the two situations. Could it be done with a series?

For value h := 6.62607015*10^(-34); c := 299792458; T := 273 + 24; k := 1.380649*10^(-23);

ec := 1.602176634*10^(-19); ν1 :=10¹² ; ν2 := 10¹⁷ ;Tq := 1.765358264*10^(-19);

Could it be merged E2 into one plot for ν = 10¹² .. 10¹⁷? 

PPh1.mw

How can I solve Einstein’s equation and calculus of the value of the K constant in Einstein's equation and the value of the tensor stress energy that fits in this equation?

QTBend.docxSqBend.mw

elctroWav.mw have the equation 1 :

eq1 := 2*m*(E + e0^2/(rb*rho))*g(rho, t)*(-rb*rho + R)/(h^2*R) + R*(diff(g(rho, t), rho, rho)*(-rb*rho + R)/R - 2*diff(g(rho, t), rho)*rb/R)/(rb^3*rho) - diff(g(rho, t), t, t)*(-rb*rho + R)/(a^2*c^2*R) = 0;

with iv1:

iv1 := D[1](g)(0, 0) - g(0, 0)*rb/R = rb*R, g(1, 0)*(R - rb)/R = 0, D[2](g)(rb, 0) = a*c;

As in maple document electroWav.mw

The issue is that there is an unsolved part with RootOf how can I rezolve it?

-R*h^2*RootOf(AiryBi(-(R*_Z^3*h^2 + 2*e0^2*m*rb^2)/(_Z^2*R*h^2)))^3

Please advice...

How do I solve completely the diferential equation and also speed up the compilation of  the time is over 3000sec: 

eq1 := 2*m*(E + 8*Pi*epsilon/r)*f(r, t)/h^2 + R*diff(f(r, t), r $ 2)/r - diff(f(r, t), t $ 2)/(a^2*c^2) = 0;

iv1 := f(r, 0) = 0, f(R, t) = 0, D[1](f)(0, 0) = R;

Sol := pdsolve([eq1, iv1]);

Where f(r,t) is the function of variable r and t  in spherical coordinate and m, E, h, R, rb, a, and c are constants.

I also want to find the exact value of f(r,t) with the condition f(rb, 0) = 0; and diff(f(rb,t),t)=a*c for the value t=0 and if is possible the pulsation of the sinusoidal solution of f(r,t). [the solution is a combination of AiryAi ; AiryBi and sinusoidal sin(a*c*sqrt(-2*E*m - _c[1])*t/h)]. I didn't find the value of _c[1] for the 2 additional condition above.

The issue is the period of time between 2 consecutive zero of the f(r,t)=0

tks