Homework Help: 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

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

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