let me apologize in advance for not using latex

one of my students (I'm an english teacher in japan) mentioned one of the DE's he had tried to solve way back in the day when he was a chemical engineer. He often had trouble and went to his math friend for help. Being a typical mathematician, his friend would ponder the problem for a few moments and then say confidently that there was indeed a solution. Of course he never actually wrote one out.

now I find myself in a similar situation...

To start, a simple DE:

dB/dt = k1*(B +k2)^0.6 * B^0.8 [B is the concentration of something, k1, k2 constants]

next part is easy:

(k1*(B +k2)^0.6 * B^0.8)^-1 dB = dt and we just integrate. easy, right?

int[(B +k)^-0.6 * B^-0.8] dB = t <I dropped the k1> but how can we actually perform this integration?

I banged my head a couple times, but couldn't think of any nice substitution.

I'm thinking that maybe there is a pretty way to do this using contour integration, but I haven't come up with anything yet...

Maple is no help.

Any thoughts?

one of my students (I'm an english teacher in japan) mentioned one of the DE's he had tried to solve way back in the day when he was a chemical engineer. He often had trouble and went to his math friend for help. Being a typical mathematician, his friend would ponder the problem for a few moments and then say confidently that there was indeed a solution. Of course he never actually wrote one out.

now I find myself in a similar situation...

To start, a simple DE:

dB/dt = k1*(B +k2)^0.6 * B^0.8 [B is the concentration of something, k1, k2 constants]

next part is easy:

(k1*(B +k2)^0.6 * B^0.8)^-1 dB = dt and we just integrate. easy, right?

int[(B +k)^-0.6 * B^-0.8] dB = t <I dropped the k1> but how can we actually perform this integration?

I banged my head a couple times, but couldn't think of any nice substitution.

I'm thinking that maybe there is a pretty way to do this using contour integration, but I haven't come up with anything yet...

Maple is no help.

Any thoughts?

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