令 y ' = p = dy / dx,則 y'' = dp / dx = dp/dy * dy/dx = dp/dy * p,代入原方程得到：
y^2 * dp/dy * p + 1 = 0 => -pdp = 1/y^2 dy
兩邊同時積分上式得到：
-1/2 p^2 = -1/y + C1 => p^2 = 2/y + C1 (仍用C1記常數(shù))
該積分曲線過點(diǎn)(0,1/2),且該點(diǎn)的切線斜率為2,代入上式有：
2^2 = 4 + C1 => C1 = 0 => p = dy/dx = √(2/y) => √y dy = √2 dx
積分上式化簡即有：
x = √2/3 * y^(3/2) + C2
過點(diǎn)(0,1/2),代入得到：C2 = -1/6,所以積分曲線：
x = √2/3 * y^(3/2) - 1/6