Finding Non-Linear Terms of Linear Function Equation

[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?

 

[Integral]

What do you have for a definition of linear?

 

[UrbanXrisis]

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

 

[topsquark]

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

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

-Dan

 

[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.

 

[UrbanXrisis]

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

 

[topsquark]

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

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

-Dan

 

[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?

 

[HallsofIvy]

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

 

[UrbanXrisis]

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

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

 

[topsquark]

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

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

Yep!

-Dan