Construct the intermediate steps in the derivation of the equation for the

value of a risky bond $($when a Poisson process governs the default$)$:

$\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{t}}+\frac{1}{2}{w}^2\frac{de{l}^{2}V}{del{r}^2}+(u-w)\frac{\text{d}\text{e}\text{l}\text{V}}{\text{d}\text{e}\text{l}\text{r}}-(r+)V=0$