Boundary Value Problems/ODE BVPs

Two point BVPs for an ODE

Begin with second order DEs, $x^{″}=f(t,x,x^{\prime })$, with conditions on the solution at $t=a$ and $t=b$.

$\frac{d^{2}x}{d{t}^2}+p(t)\frac{dx}{dt}+q(t)x(t)=f(t)$ with $a_{0}x(a)+a_1{x}^{\prime }(a)=g$ and $b_{0}x(b)+b_1{x}^{\prime }(b)=h$ on the interval $I_{ab}=\{x|a\le t\le b\}$

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Example

$\frac{d^{2}x}{d{t}^2}+4\frac{dx}{dt}+2x(t)=f(t)$ with $x(0)=0$ and $x(1)=0$ on the interval $I_{ab}=\{x|0\le t\le 1\}$