Separable Differential Equation dy/dt = 6y The question is as follows: (dy)/(dt)=6y y(9)=5

klasyvea 2022-11-19 Answered
Separable Differential Equation dy/dt = 6y
The question is as follows:
d y d t = 6 y
y ( 9 ) = 5
I tried rearranging the equation to d y 6 y = d t and integrating both sides to get ( 1 / 6 ) ln | y | + C = t. After that I tried plugging in the 9 for y and 5 for t and solving but I can't quite seem to get it.
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Answers (1)

Lena Gomez
Answered 2022-11-20 Author has 14 answers
1 6 ln | y | = t + C I would be inclined to not solve for C at this time.
You could say
1 6 ln | 5 | = 9 + C C = 1 6 ln | 5 | 9
Notice that C just stays C. 6C,C, it is just an arbitrary constant.
y = e 6 t + C y = e C e 6 t y = C e 6 t
I did it again! And once you have done these for a week, you will drop the intermediate steps and go:
1 6 ln | y | = t + C y = C e 6 t
We have to find C now.
y ( 9 ) = 5 5 = C e 54 C = 5 e 54 y = 5 e 54 e 6 t
or
y = 5 e 6 t 54
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