Problem $1$

Compute the following indefinite integral:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2+1}{x}+7sin(3x)dx$

Problem $2$

Consider the differential equation:

$\frac{dy}{dx}=e^{-3x}$

with the initial condition $y(0)=\frac{2}{3}.$

Solve the initial value problem.

Determine if this differential equation reaches a steady state.