II Summer $5/27-8/15/2025$

Question $5,11\mathrm{.}4\mathrm{.}35$

$4$ Working With Taylor Series

Part $2$ of $2$

Consider the differential equation $y^{\text{'}}(t)-3y(t)=10,y(0)=4.$

a$.$ Find a power series for the solution of the differential equation.

b$.$ Identify the function represented by the power series.

a$.$ Choose the correct answer below.

A$.y(t)=1022t33t^{2}33t^3$ dots $\frac{22*3^{n-1}}{n!}{t}^n$ dots

B$.y(t)=422t33t^{2}33t^3$ dots $\frac{22*3^{n-1}}{n!}{t}^n$ cdots

c$.y(t)=10-22t33t^2-33t^3$ dots $\frac{(-1{)}^{n}22*3^{n-1}}{n!}{t}^n$ dots

D$.y(t)=4-22t33t^2-33t^3$ cdots $\frac{(-1{)}^{n}22*3^{n-1}}{n!}{t}^n$ cdots

b$.y(0)=$

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