Solving ODE's with a and b parameters: Methods and Tips

[Damascus Road]

Hey all,

I have these 2 ODE's that I have to solve:

$$a.) y' = ay - by^{3} ; a,b > 0$$
$$b.) y' = (a cos(x) + b)y - y^{3}$$I'm not even exactly sure what method to use for these...

I tried splitting up the variables in a.) but it got kinda messy:

$$\int \frac{dy}{y(a-by^{2})} = \int dx$$

Is there a better way to approach it?
A method suggestion for b.) would be great!

 

[tiny-tim]

Hi Damascus Road!

For a.) use partial fractions on 1/y(a-by²)

For b.) … I've no idea