Chapter 9.4, Problem 3E

Use Ito’s formula to show that the solutions of the SDE initial value problems $\begin{array}{l}\text{a}\text{. }\{\begin{array}{c}dy=tydt+e^{t^2/2}d{B}_t\\ y(0)=1\end{array}\\ \text{b}\text{. }\{\begin{array}{c}dy=3\left(B\begin{array}{c}2\\ ta\end{array}\right)d{B}_t\\ y(0)=0\end{array}\end{array}$ are (a) $y(t)=\left(1+B_t\right)e^{t^2/2}$ (b) $y(t)=B\begin{array}{c}3\\ t\end{array}-3t{B}_t$.