What is the general solution of the differential equation dy/dx+2y=0?

Paul Reilly 2022-09-12 Answered
What is the general solution of the differential equation d y d x + 2 y = 0 ?
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Answers (1)

zagrebova1c
Answered 2022-09-13 Author has 10 answers
We have:

d y d x + 2 y = 0

We can just rearrange as follows:

d y d x = - 2 y 1 y   d y d x = - 2

This is a first Order Separable Differential Equation and "separate the variables" to get

  1 y   d y =   - 2   d x

And integrating gives us:

ln | y | = - 2 x + A

| y | = e - 2 x + A

Note that as e α > 0 α , we can write

y = e - 2 x + A
    = e - 2 x e A
    = C e - 2 x
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