help with lowering the derivative of an ODE

[math424]

Hi all,

I am going to evaluate the fist derivative of function psi (which satisfies the following ODE).

with psi=d(psi)/dy=0 as y goes to infinity.
Interestingly, if a=1 (it means if right-hand-side of the above ODE is in form of sinh(psi)), first derivative of psi can be expressed as

So, I was wondering if it is possible to express d(psi)/dy in case of arbitrary a.

Thanks!

 

[math424]

Hi all,

I am going to evaluate the fist derivative of function psi (which satisfies the following ODE).
View attachment 4138
with psi=d(psi)/dy=0 as y goes to infinity.
Interestingly, if a=1 (it means if right-hand-side of the above ODE is in form of sinh(psi)), first derivative of psi can be expressed as
View attachment 4139
So, I was wondering if it is possible to express d(psi)/dy in case of arbitrary a.

Thanks!

never mind, found the solution!