Questions

01

Linear operator

Show that the example differential operator above satisfies the linearity equation for two given functions $y_1(x)$ and $y_2(x)$. Let $F=\left(\frac{d^2}{d{x}^2}-x\right)$; show that:

$$F(a{y}_1+b{y}_2)=aF(y_1)+bF(y_2).$$