# Linear functions

1. Mar 5, 2006

### UrbanXrisis

having the following equation, where F(x) is a function, and c is a constant independent of x, i am to find the non linear terms of the equation:

$$cF(x)\frac{dF(x)}{dx}+\frac{d^2F(x)}{dx^2}+ic^2 \left (\frac{1}{F(x)}+F(x) \right) =0$$

i'm not sure where to start or start. could someone guide me in the right direction?

2. Mar 5, 2006

### Integral

Staff Emeritus
What do you have for a definiton of linear?

3. Mar 5, 2006

### UrbanXrisis

functions where x is raised to the first power? is this the definition that i should use?

Last edited: Mar 5, 2006
4. Mar 5, 2006

### topsquark

I think what Integral meant was "What is the definition of a linear ordinary differential equation?"

-Dan

5. Mar 5, 2006

### HallsofIvy

Staff Emeritus
Or, to put it another way, before you can decide which terms are non-linear, you have to know what "non-linear" terms look like! If you understand what "non-linear" and "linear" terms are you should be able to look at the equation and write down the answer without any computation.

6. Mar 5, 2006

### UrbanXrisis

linear ordinary differential equation should be in the form a(x)y''+b(x)y'+c(x)y=d(x)

7. Mar 5, 2006

### topsquark

So calling y=F(x), what terms in your original equation don't look linear?

-Dan

8. Mar 5, 2006

### UrbanXrisis

my equation would then become:

y''+cy(x)y'+ik^2/y+y=0

the non linear part is then: $$\frac{ic^2}{F(x)}$$

right?

9. Mar 6, 2006

### HallsofIvy

Staff Emeritus
No. There is another non-linear term in there. Remember it is not just y that counts but derivatives of y also.

10. Mar 6, 2006

### UrbanXrisis

$$y''+cyy'+\frac{ic^2 }{y}+ic^2y =0$$

so do you mean cyy' is a non-linear term too along with $$\frac{ic^2 }{y}$$?

11. Mar 6, 2006

Yep!

-Dan