- #1
skyturnred
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Homework Statement
Solve:
y'=x+y, y(0)=2
Homework Equations
The Attempt at a Solution
I THINK my method is correct.. but I messed up somewhere.
I rearrange for y'-y=x
integrate both sides gets me:
y-[itex]\frac{y^{2}}{2}[/itex]=[itex]\frac{x^{2}}{2}[/itex]
after completing the square I get
(y-1)[itex]^{2}[/itex]=-x[itex]^{2}[/itex]+1
But this is where I mess up. To solve for y, I square root each side. But then I get '+ or -' on the right side:
y=[itex]\pm[/itex][itex]\sqrt{-x^{2}+1}[/itex]+1+c
so solving for both cases gets me c=0 OR c=2. But I can only have once answer. Where did I go wrong?
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