find the general solution of the following equation. express the solution explicitly as a function of the…

Explanation:

Step1: Rewrite the equation

Rewrite $t^{-7}y'(t)=1$ as $y'(t)=t^{7}$. Recall that $y'(t)=\frac{dy}{dt}$, so we have $\frac{dy}{dt}=t^{7}$.

Step2: Integrate both sides

Integrate $\int dy=\int t^{7}dt$. Using the power - rule for integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$), for the right - hand side $\int t^{7}dt=\frac{t^{7 + 1}}{7+1}+C=\frac{t^{8}}{8}+C$, and $\int dy=y$.

Answer:

$y=\frac{t^{8}}{8}+C$