## Elementary Differential Equations and Boundary Value Problems 9th Edition

General form of second order differential boundary value problem: $\mathcal{p}$($\mathcal{x}$)$\mathcal{y^{n}}$$\mathcal{+}$$\mathcal{q(x)y^{1}+r(x)y=g(x)}$ $\mathcal{y(x_{0})=y_{0}}$ $\mathcal{y(x_{1})=y_{1}}$ Equation is homogeneous if $\mathcal{g(x)}$ and $\mathcal{y_{0}=y_{1}=0}$ $\mathcal{-y^n+\leftthreetimes(1+x^2)y}$ $\mathcal{-y^n-\leftthreetimes(1+x^2)y=0}$ Since $\mathcal{g(0)}$=$\mathcal{0}$, $\mathcal{y_0=y_1=0}$ equation is homogeneous