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

klasyvea

klasyvea

Answered question

2022-11-19

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.

Answer & Explanation

Lena Gomez

Lena Gomez

Beginner2022-11-20Added 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

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?