# Question:How do I solve completely this differential equation in Maple?

## Question:How do I solve completely this differential equation in Maple?

Maple

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

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