Solve this nonlinear, second order ODE

[KillerCharlie]

y'' = C1 - C2 * (y')^2

C1, C2 are constants
y is the dependent variable
let x be in independent variable
This is an IVP with y(0) and y'(0) known

This is not directly a homework problem. This DE is used in a much larger computer program. Currently it's being solved numericaly with an RK4 routine. This program is called by an optimizer several hundred times, so it'd be nice to cut down on running the RK routine every time and also not have to worry about step size (currently using constant step size).

 

[KillerCharlie]

Wow, I actually just found the solution in a DifEq book after looking through it for the third time... the answer involves cosh and tanh and will numerically blow up if you set C2 to zero.

 

[z0mb13]

I totally forgot about this!!!

 

[ruffilb]

Noooooooooo idea what this is...

 

[Codegen]

Edit: Multiple Post

 

[Codegen]

You know you're a computer nerd when you read "IDE"

Edit: Grammar error

 

[KillerCharlie]

Originally posted by: Codegen
You know your a computer nerd when you read "IDE"

You know you're a true nerd/geek when you read ODE.

Anyway, we looked at the equation again and it turns out that we forgot a term so now it's highly nonlinear... 🙁