1. Separable DE

For the equation above, I need to find all the constant solutions. How do I go about doing this? I've tried putting all similar terms on one side and then integrating, but it doesn't seem to work out nicely. Any help is greatly appreciated, thanks in advance!

2. $\int y' = \int y-y^3$

$\Rightarrow y= \frac{2y^2 - y^4}{4} + C$

$\Rightarrow \frac{y}{4}(y^3-2y+4)=C$

$\Rightarrow \frac{y}{4}(y^3-2y+4)-C=0$

Code:
syms y c
solve('(y/4)*(y^3-2*y+4)-c=0',y)

ans =

- 1/6/(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/6)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 1/6/(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/6)/(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/4)*(48*c*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 4*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) + 24*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) + 48*6^(1/2)*(3*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 36*c + 26)^(1/2))^(1/2)
1/6/(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/6)/(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/4)*(48*c*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 4*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) + 24*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) + 48*6^(1/2)*(3*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 36*c + 26)^(1/2))^(1/2) - 1/6/(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/6)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2)
1/6/(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/6)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 1/6/(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/6)/(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/4)*(48*c*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 4*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) + 24*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 48*6^(1/2)*(3*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 36*c + 26)^(1/2))^(1/2)
1/6/(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/6)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) + 1/6/(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/6)/(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/4)*(48*c*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 4*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) + 24*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3)*(12*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(1/3) - 48*c + 9*(8/9*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 32/3*c + 208/27)^(2/3) + 4)^(1/2) - 48*6^(1/2)*(3*3^(1/2)*(64*c^3 + 32*c^2 - 68*c + 25)^(1/2) - 36*c + 26)^(1/2))^(1/2)
umm... lol. Your sure your not given any initial conditions, $y(x)=0?$

3. that's wrong, the ODE actually writes as $\frac{dy}{y-y^{3}}=dx,$

4. Originally Posted by Krizalid
that's wrong, the ODE actually writes as $\frac{dy}{y-y^{3}}=dx,$
Figured it had to be . So your pretty good at calc, huh?

5. uhh yeah there aren't any initial conditions

6. Originally Posted by cdlegendary

For the equation above, I need to find all the constant solutions. How do I go about doing this? I've tried putting all similar terms on one side and then integrating, but it doesn't seem to work out nicely. Any help is greatly appreciated, thanks in advance!
if $y = C$ , then $y' = 0$ ... correct?

7. Originally Posted by skeeter
if $y = C$ , then $y' = 0$ ... correct?
ah yes. I think I know where you're going with that

8. so the solutions are just -1, 0, 1. wow haha. I was definitely thinking too hard about that. thanks!