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pachaquis3s

pachaquis3s

Answered question

2022-06-25

If I have: σ ˙ ( t ) = γ σ ( t )
where γ is a constant, the solution is given by:
σ ( t ) = σ ( 0 ) e γ t
Now what if I have the differential equation: σ ˙ ( t ) = γ x ( t ) σ ( t )
Then is the solution given by:
σ ( t ) = σ ( 0 ) e γ x ( t ) t
Or...?

Answer & Explanation

Amy Daniels

Amy Daniels

Beginner2022-06-26Added 20 answers

Say I do something like this:
σ ˙ ( t ) σ ( t ) = γ x ( t ) .
can you integrate both sides? What do you get on the left side? What do you get on the right side?
(In case it's confusing, the answer will have something like x ( t ) d t in it.)

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