Is a solution of a differential equation a function of its parameters?

[Meaning]

Hi everyone,

Imagine I have a system of linear differential equations, e.g. the Maxwell equations.

Imagine my input variables are the conductivity $\sigma$. Is it correct from the mathematical point of view to say that the electric field solution, $E$, is a function of sigma in general, E(r,t,sigma)?

Thank you

 

[pasmith]

Yes. Unless something weird is going on, the value of the solution at a particular point and time is determined by the parameters and the initial and boundary conditions.

 

[Meaning]

Yes. Unless something weird is going on, the value of the solution at a particular point and time is determined by the parameters and the initial and boundary conditions.

Thank you

 

[jedishrfu]

Basically, any differential equation describes a family of curves, surfaces, volumes...

It's the boundary conditions and initial parameters that fix it to one curve, surface or volume...