Linear: $$ \frac{d^2y}{dx^2} + P(x)\frac{dy}{dx} + Q(x)y = F(x).$$
* Can divide through by $k(x)$ to show the linear form above with $P(x)$, $Q(x)$, $F(x)$.
Nonlinear:
Examples for heat conduction:
Examples: heat conduction.
put in a value, solve an ODE IVP, take the difference between the known BC, and the BC you got with the guess. Return that difference.
boundary | T | z |
---|---|---|
x=0 | $T_L$ | ? |
x=H | $T_R$ | ? |
But with a function that involves solving an ODE and then checking the resulting boundary condition against the specified boundary condition.