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

find the general solution of the following equation. express the solution explicitly as a function of the independent variable. t^(-8)y(t)=2 y=

find the general solution of the following equation. express the solution explicitly as a function of the independent variable. t^(-8)y(t)=2 y=

Answer

Explanation:

Step1: Isolate $y'(t)$

$y'(t)=2t^{8}$

Step2: Integrate both sides

$y(t)=\int 2t^{8}dt$ Using the power - rule for integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$), we have $y(t)=2\times\frac{t^{9}}{9}+C=\frac{2}{9}t^{9}+C$

Answer:

$\frac{2}{9}t^{9}+C$