How to solve first order ode with two boudary conditions?

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I need to solve numericaly differential equation of the first order, where I have given values at the beginng and at the end of time span, it means I have p(t=0) = 0, p(t=1) = 0. My differential equation where p is variable for which I am looking for is:
p' = - ( - 8 .* y' ./ R - y' .* p - 32 .* beta .* k ./ R .^ 4 ) ./ y
and k is also unknown variable, and R, beta, y, y' are known variables
I tryed to solve it and get p with bvp4c, but I found only examples where differential equations of the second order where solved, with conditions in two end points, and it should be like that - for second order equation two conditions.
I was looking ode45 also, but there you can give time span and the conditions at the end of that span, it means I could give only one condition here.
For what I should search for? Did I miss something in this case?
darova on 27 Mar 2020
Are you sure about all you constants/parameters? Maybe you want to fit some? Look this

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