What is the general solution of the differential equation dy/dx+y=xy^3?

redolrn 2022-09-27 Answered
What is the general solution of the differential equation d y d x + y = x y 3 ?
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Answers (1)

Derick Ortiz
Answered 2022-09-28 Author has 11 answers
Making the change of variable y = 1 z we have the new version
d y d x + y - x y 3 = 0 x - z 2 + z z z 3 = 0 or
x - z 2 + z z = 0
Now calling ξ = z 2 we have
x - ξ + 1 2 ξ = 0
Solving for ξ we obtain easily
ξ = 1 2 + x + C e 2 x = z 2 then
z = ± 1 2 + x + C e 2 x = 1 y then finally
y = ± 1 1 2 + x + C e 2 x
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