# I have a tough d.e.

• May 27th 2008, 09:26 AM
you
I have a tough d.e.
My professor and I are working on a d.e., and I was wondering if anyone here could solve it:
$\displaystyle dx/dt=(1-x)[x-f(t)]$ where f is some function of only t. Maple gives us a solution, but we want to be able to solve it for ourselves.
• May 27th 2008, 01:26 PM
NonCommAlg
Quote:

Originally Posted by you
My professor and I are working on a d.e., and I was wondering if anyone here could solve it:
$\displaystyle dx/dt=(1-x)[x-f(t)]$ where f is some function of only t. Maple gives us a solution, but we want to be able to solve it for ourselves.

it's a Riccati d.e. put $\displaystyle x=1+\frac{1}{y}$ to get $\displaystyle \frac{dy}{dt}+(f(t)-1)y=1,$ which is a simple linear d.e.

Q.E.D.
• May 28th 2008, 09:44 AM
you
Quote:

Originally Posted by NonCommAlg
it's a Riccati d.e. put $\displaystyle x=1+\frac{1}{y}$ to get $\displaystyle \frac{dy}{dt}+(f(t)-1)y=1,$ which is a simple linear d.e.

Q.E.D.

Thanks, that helped a lot :)