# Thread: I have a tough d.e.

1. ## 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:
$dx/dt=(1-x)[x-f(t)]$ where f is some function of only t. Maple gives us a solution, but we want to be able to solve it for ourselves.

2. Originally Posted by you
My professor and I are working on a d.e., and I was wondering if anyone here could solve it:
$dx/dt=(1-x)[x-f(t)]$ 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 $x=1+\frac{1}{y}$ to get $\frac{dy}{dt}+(f(t)-1)y=1,$ which is a simple linear d.e.

Q.E.D.

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

Q.E.D.
Thanks, that helped a lot