Recall that Newton's Law of cooling is given by the differential equation

$\frac{dH}{dt}=-k(H-H_s)$

where $H$ is the heat of the object, $H_s$ is the ambient$/$surrounding temperature of the environment, and $k$ is the proportionality constant dependent on the materials involved.

$($i$)$ Compute the explicit general solution to Newton's Law of Cooling for a proportionality constant of $k=3$ and an ambient temperature of $H_s=26(C)$

$($ii$)$ Solve the initial value problem for the explicit particular solution given by $H(2)=44(C).$