Solve the differential equation dy/dx+y=0 ?

Aidyn Meza 2022-09-27 Answered
Solve the differential equation d y d x + y = 0 ?
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Answers (1)

elilsonoulp2l
Answered 2022-09-28 Author has 9 answers
We can rewrite the equation:

d y d x + y = 0

as:

d y d x = - y 1 y d y d x = - 1 `

Which is a First Order linear separable Differential Equation, so we can "separate the variables" to get:

  1 y   =   - 1   d x

Which we can integrate to get:

ln | y | = - x + c

Taking Natural logarithms we then get:

| y | = e - x + c

As e x > 0 x we then get:

y = e - x + c
    = A e - x

We can easily verify the solution:

y = A e - x y = - A e - x
y + y = - A e - x + A e - x = 0       Q E D
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