- #1
Saladsamurai
- 3,020
- 7
I am reading through my Diff Eqs Text and I follow most of the lingo. However I am just a tad confused by the statement:
An nth order ODE is said to be linear if F is linear in y,y',...y^(n)
Then it gives the example:
[tex]a_n(x)\frac{d^ny}{dx^n}+a_{n-1}(x)..+a_0(x)y=g(x)[/tex]
It then says: 'On the left-hand side of the above equation the dependent variable y and all of its derivatives, y,y',y'',...y[itex]^n[/itex] are of the first degree.
Clearly I missed something in Calc. If n=2, I have: [tex]\frac{d^2y}{dx^2}[/tex]
Why is this linear if n=2?
Thanks,
Casey
An nth order ODE is said to be linear if F is linear in y,y',...y^(n)
Then it gives the example:
[tex]a_n(x)\frac{d^ny}{dx^n}+a_{n-1}(x)..+a_0(x)y=g(x)[/tex]
It then says: 'On the left-hand side of the above equation the dependent variable y and all of its derivatives, y,y',y'',...y[itex]^n[/itex] are of the first degree.
Clearly I missed something in Calc. If n=2, I have: [tex]\frac{d^2y}{dx^2}[/tex]
Why is this linear if n=2?
Thanks,
Casey