- #1
Shannabel
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Homework Statement
If (x^2+1)dy/dx = xy for all y>0, and y(2) = 5, then y(3) = ?
Homework Equations
The Attempt at a Solution
dy/y = xdx/(x^2+1) -- use substitution with u=x^2
lny = 2(u+1)/du
lny = 2ln(x^2+1)+c
y = e^(2ln(x^2+1)+c)
5 = e^(2ln(5)+c)
5 = e^(ln25+c)
5 = 25+c
c = 20
y(3) = e^(2ln10+20)
= e^ln100+20
= 100+20
= 120
... the answer should be 5sqrt(2), so I am very off, but I can't find why. help?