- #1

CaptainJames

- 18

- 0

## Homework Statement

x^2y' + 2xy = 5y^3

## Homework Equations

Bernoulli Equation

## The Attempt at a Solution

so... v=y^-2, y=v^(-1/2) y' = -1/2v'v^(-3/2)

moving everything over...

y'/y^3 + 2/(xy^2) = 5/x^2

and plugging everything in...

-1/2v' + 2v/x = 5/x^2

v' - 4v/x = -10/x^2

v' - 4v/x = 0

dv/dx = 4v/x

dv/v = 4dx/x

ln v = 4 ln x + C

v = C(x)x^4

v' = C'(x)x^4 + C(x)4x^3

C'(x)x^4 + C(x)4x^3 - 4C(x)x^4/x = 5/x^2

C'(x)x^4 = 5/x^2

C'(x) = 5/x^6

C(x) = -x^-5 + C

v = (-x^-5 + C)x^4

y = 1/(v)^(1/2)

y^2 = 1/((-x^-5 + C)x^4)

... which is wrong. Could someone point me in the right direction?