Answer
Homogeneous.
Work Step by Step
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
