Differential Equation: y' = y-y^3. I've got it down to:

y^2 - 2y = e^(2t) e^c

But the problem is: List all constant solutions for the DE

I don't quite get how to get any further. x_x

Question

Differential Equation: y' = y-y^3.  I've got it down to:

y^2 - 2y = e^(2t) e^c

But the problem is: List all constant solutions for the DE

I don't quite get how to get any further. x_x

jamesj · Answer

If y' = y - y^3 then
$$ \frac{dy}{y(1-y^2)} = dx $$
Now integrate and you'll find the expression you've written down isn't quite right.

anonymous · Answer

oh :c  Lemme redo it. @_@  What does a 'constant solution' mean, though?  Is that the same thing as equilibrium solution?

anonymous · Answer

I get a really weird solution full of radicals...

anonymous · Answer

Constant solutions are the same as the equilibrium solutions

anonymous · Answer

*facepalm* Constant solution is equilibrium solution. I'm stupid and didn't read the problem right. didn't even need to do the actual integration Q_Q  Sorries. I have the answer now :3

jamesj · Answer

Ah, well, a constant is a solution if y' = 0.  I.e., y - y^3 = 0 => y = 0, 1 or -1.

anonymous · Answer

:) be glad you don't have to, that dq is real dirty

anonymous · Answer

Thank you~  That's exactly what I got O:

anonymous · Answer

@Fronklin Yea ;_;  I forgot how to do integration by parts aha...