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y`+2y=y^2

my problem:

suppose u=1/y

so u`=-[y^(-2)]*y`=-1+2u

so du/(1+2u)=-dx

=>1+2u=ce^(-x)

=>u=[1-ce^(-x)]/2

so y=1/u=2/[1-ce^(-x)]

but the correct answer should be y=x/[1+2cx^(2x)]

does anybody know where my calculations went wrong?

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# ODE y`+2y=y^2

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