Hi,

Anyone can advise how the above equation can be solved?

Thanks.

wee

Printable View

- Feb 27th 2008, 12:35 AMweeSolve dy/dt = 2y + 1 - (9/16)y^2
Hi,

Anyone can advise how the above equation can be solved?

Thanks.

wee - Feb 27th 2008, 01:50 AMPeritus
This is a simple Riccati equation:

now it is easy to see that y= 4 and y = -4/9 are particular solutions to this equation, the following substitution allows us to find the general solution:

let's choose

thus:

which is a Bernoulli equation. The substitution that is needed to solve this Bernoulli equation is:

thus we get:

which is a linear first order ODE, and can be easily solved using the integrating factor method. After you finish just back substitute twice to obtain the final solution... - Feb 27th 2008, 06:42 AMKrizalid
You can treat it like a separable equation too. (It's not so bad.)

After some simple calculations we have where (or another letter you want) as usually is the constant. - Feb 27th 2008, 06:21 PMwee
Thank you very much.

I got it now.