Find a Taylor expansion for the solution $x(t)=a_{0}+a_{1} t+a_{2} t^{2}+\cdots$ for the differential equation $\frac{d x}{d t}=t \cdot x$ with the boundary condition $x(0)=1$. Solve for $\left\{a_{0}, a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\right\} .$ Do this by hand solving for these coefficients recursively. Solve for the coefficients using the Taylor Method program included in your program collection. Can you determine the general $a_{n} ?$