# Solve Differential Equation with Boundary Conditions (lengthy equation)

I have a lengthy equation to be substitute into a differential equation. I used DSolve to generate the output. However, it took me more than 3 hours and it still running. The DE is the convective-diffusion equation which is

`1/r del /del r (r del f1s/ del r) - a1 = 0`

and the boundary condition is `r=k` when `del f1s/ del r =0`

so the input is:

``a1 = -(810165067720210957064125/25546163167349695028752149) -       0.00395833 (-0.5 + r) (1.02817 +          3.98107/(5.36839*10^11/r - 1.*10^12 r)^(1/20) +          2./((1.27718 - 0.666667 r - 0.333333 r^2)/(1. + r))^(1/20) +          3./((3.05377 - 0.888889 r - 0.111111 r^2)/(4. + r))^(1/20) +          3.01772/(-((1. (-0.675531 + 0.125 r + r^2))/(0.0625 + r)))^(         1/20) + 3.03794/(-((1. (-0.867019 + 0.285714 r + r^2))/(           0.142857 + r)))^(1/20) +          2.04096/(-((1. (-1.14539 + 0.5 r + r^2))/(0.25 + r)))^(1/20) +          3.08948/(-((1. (-1.57936 + 0.8 r + r^2))/(0.4 + r)))^(1/20) +          3.12414/(-((1. (-2.32712 + 1.25 r + r^2))/(0.625 + r)))^(1/20) +          3.23431/(-((1. (-7.80849 + 3.5 r + r^2))/(1.75 + r)))^(1/20)) +       0.125 (-0.5 + r) (0.196614 +          1.32702*10^-12 (5.36839*10^11/r - 1.*10^12 r)^(19/20) +          0.666667 ((1.27718 - 0.666667 r - 0.333333 r^2)/(1. + r))^(          19/20) + ((3.05377 - 0.888889 r - 0.111111 r^2)/(4. + r))^(         19/20) +          0.894139 (-((1. (-0.675531 + 0.125 r + r^2))/(0.0625 + r)))^(          19/20) +          0.787613 (-((1. (-0.867019 + 0.285714 r + r^2))/(0.142857 + r)))^(          19/20) +          0.453547 (-((1. (-1.14539 + 0.5 r + r^2))/(0.25 + r)))^(19/20) +          0.572125 (-((1. (-1.57936 + 0.8 r + r^2))/(0.4 + r)))^(19/20) +          0.462835 (-((1. (-2.32712 + 1.25 r + r^2))/(0.625 + r)))^(          19/20) +          0.239579 (-((1. (-7.80849 + 3.5 r + r^2))/(1.75 + r)))^(19/20))   TRY = DSolve[{1/r D[r f1s'[r], r] - a1 == 0, f1s'[k] == 0}, f1s, r, GeneratedParameters -> S] ``

I’m stuck and I don’t know what else should I do. I tried to do manually by integrating the equation but it’s kinda haywire. Could anyone help me out with this coding. Really appreciate it ðŸ™‚