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October 30th, 2014, 09:19 AM   #1
shy
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solution for integral..dy/dx=a/(x^(1/2))+b/y

hi everyone!
I am trying to have an explicit solution for the ode:
dy/dx=a/(x^(1/2))+b/y

It would be awsome if someone has an idea of how to solve it i tried some stuff buy I have quite poor integration abilities.
I tried only in matlab and it doesnt have an explicit solution,
I wonder if human fine brain can be more elegant?
many thanks
Shy
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October 30th, 2014, 07:08 PM   #2
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Quote:
Originally Posted by shy View Post
hi everyone!
I am trying to have an explicit solution for the ode:
dy/dx=a/(x^(1/2))+b/y

It would be awsome if someone has an idea of how to solve it i tried some stuff buy I have quite poor integration abilities.
I tried only in matlab and it doesnt have an explicit solution,
I wonder if human fine brain can be more elegant?
many thanks
Shy
Not likely. We're going to have to solve an equation with ln(y) and atn(y) both in it. There is no closed form solution...you'll have to solve it numerically.

-Dan
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October 30th, 2014, 11:39 PM   #3
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Hi shy !
The solution cannot be expressed on the form y(x), but on an implicit form :
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