Chapter A.5, Problem 1P

In Problems 1 through 8, compute the successive approximation formula to compute $y_n\left(x\right)$ for $n\underset{\_}{\le }4$. Then write the exponential series for which these approximations are partial (perhaps with rile first term or two missing; for example, $e^x-1=x+\frac{1}{2}{x}^2+\frac{1}{6}{x}^3+\frac{1}{24}{x}^4+\mathrm{...}$ ).

$\frac{dy}{dx}=y,y\left(0\right)=3$