令u = dy/dx,du/dx = d²y/dx²
du/dx•(1 + e^x) + u = 0
du/dx•(1 + e^x) = - u
du/(u) = -1/(1 + e^x),两边积分
ln|u| = ln(1 + e^-x) + C₁
u = C₁(1 + e^-x)
dy/dx = C₁(1 + e^-x),两边积分
y = C₁(x - e^-x) + C₂
令u = dy/dx,du/dx = d²y/dx²
du/dx•(1 + e^x) + u = 0
du/dx•(1 + e^x) = - u
du/(u) = -1/(1 + e^x),两边积分
ln|u| = ln(1 + e^-x) + C₁
u = C₁(1 + e^-x)
dy/dx = C₁(1 + e^-x),两边积分
y = C₁(x - e^-x) + C₂