How do you solve the differential dy/dx=x−4/√x^2−8x+1?

Janet Hart 2022-09-26 Answered
How do you solve the differential d y d x = x - 4 x 2 - 8 x + 1 ?
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Answers (1)

Lilia Horton
Answered 2022-09-27 Author has 6 answers
d y d x = x - 4 x 2 - 8 x + 1

Is a First Order separable DE which we can sole by integrating:

y =   x - 4 x 2 - 8 x + 1   d x

Let u = x 2 - 8 x + 1 d u d x = 2 x - 8 = 2 ( x - 4 )

Substituting into the RHS integral we get:

y =   1 2 u   d u
    = 1 2   u - 1 2   d u
    = 1 2 u 1 2 1 2 + C
    = u + C
    = x 2 - 8 x + 1 + C

which is the General Solution
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