- #1

cue928

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y' + (2/x)y = 5(x^-2)(y^3) v=y^-2, y=v^(-1/2), y' = -(1/2)v^(-3/2)

-(1/2)v^(-3/2)v' + (2/x)v^(-1/2) = 5x^-2(v^-3/2)

v' - (4/x)v = -10x^-2 Integrating factor: x^-4

(skipping a few mechanical steps)

vx^-4 = 2x^-5 + C

v = 2x^-1 + Cx^4

I come up with y = (2x^-1 + Cx^4)^-1/2

Problem is the book shows y^2 = x/(2+Cx^5)? What am I missing?