The solution of differential equation y '= 2x (y * Y-Y') satisfying initial condition y (0) = 1 is as follows

(1 + 2x) dy / DX = 2XY ^ 2, that is, dy / y ^ 2 = 2xdx / (2x + 1) integral on both sides is: - 1 / y = X-1 / 2 * ln (2x + 1) + C, substituting point (0,1) is - 1 = 0-0 + C, then C = - 1, that is - 1 / y = - ln (2x + 1) / 2-1, then y = 2 / (LN (2x + 1) + 2)

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