# Help with a difficult ODE

1. Jan 25, 2010

### hyime

This is really difficult for me(at least for me), though it seems simple!
Could anyone help me to solve it or give some suggestion?

y''+C1*y^2+C2*y=0

Thank you!

2. Jan 26, 2010

### tiny-tim

Welcome to PF!

Hi hyime! Welcome to PF!

(try using the X2 tag just above the Reply box )

Hint: if D represents "differentiate", then this is (D2 + C1D + C2)y = 0

3. Jan 26, 2010

### HallsofIvy

Re: Welcome to PF!

No, it isn't. The second term has $y^2$, not y'. That's a non-linear d.e. and is NOT simple.

4. Jan 26, 2010

### tiny-tim

oops!

show how it pays to write clearly!

5. Jan 26, 2010

### kosovtsov

The integrating factor to your ODE is y', so

y'(y''+C1*y^2+C2*y)=0

is an exact ODE, that is it can be presented as

(2/3*C1*y^3+C2*y^2+(y')^2)'=0

or

2/3*C1*y^3+C2*y^2+(y')^2=c

where c is an arbitrary constant. The last first order ODE (with constant coefficients) is solvable by "separation of variables".

6. Jan 26, 2010

### gato_

Look for elliptic functions and it's associated differential equation.

7. Jan 26, 2010

### hyime

Thank you for all your help, I am working on it.