The solution to the differential equation that models the temperature of the solid after t hours is given by:
D. [tex]\ln{|2H + 1|} = 2t + C[/tex]
What is the differential equation?
It is given by:
[tex]\frac{dH}{dt} = 2H + 1[/tex]
Applying separation of variables, that is, placing everything with H on one side of the equality and everything without on the other, then integrating, we find the solution.
Hence:
[tex]\frac{dH}{2H+1} = dt[/tex]
[tex]\int \frac{dH}{2H+1} = \int dt[/tex]
[tex]\frac{1}{2}\ln{|2H + 1|} = t + C[/tex]
[tex]\ln{|2H + 1|} = 2t + C[/tex]
Hence option D is correct.
More can be learned about differential equations at https://brainly.com/question/14318343
