Please help me to solve next equation: $\displaystyle x=(x^{2}-2y+1)y' $
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Originally Posted by sinichko Please help me to solve next equation: $\displaystyle x=(x^{2}-2y+1)y' $ Re-write your equation as $\displaystyle \frac{dx}{dy} = x - \frac{2y-1}{x} $ then $\displaystyle x \frac{dx}{dy} = x^2 - 2y+1 $ then let $\displaystyle u = x^2$ so $\displaystyle \frac{1}{2} \frac{du}{dy} = u - 2y + 1$ - it's linear now!
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