- #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?