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y' = (x)/(1+2y)

y(-1) = 0

trying to find the answer I do the following:

multiply both sides by (1+2y)

(1+2y) * dy/dx = x

i subtract 1 from both sides.. but for some reason this is wrong? why?

2y * dy/dx = x - 1

2y dy = x-1 dx

integrate..

y^2 = (x^2-x+C)/2

y = sqrt((x^2-x+C)/2) )

this however is wrong I was not suppose to subtract the 1 from both sides.. what exactly is wrong with doing that?

y(-1) = 0

trying to find the answer I do the following:

multiply both sides by (1+2y)

(1+2y) * dy/dx = x

i subtract 1 from both sides.. but for some reason this is wrong? why?

2y * dy/dx = x - 1

2y dy = x-1 dx

integrate..

y^2 = (x^2-x+C)/2

y = sqrt((x^2-x+C)/2) )

this however is wrong I was not suppose to subtract the 1 from both sides.. what exactly is wrong with doing that?

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