你可能就一個(gè)小技巧沒(méi)想到.
先兩邊都除以dx.
x - y(dy/dx) = x^2 * y(dy/dx) - x * y^2
y(dy/dx)讓人想到換元.
令 1/2 * y^2 = t.
那么, dt/dx = y(dy/dx)
方程變?yōu)椋?br/>x - dt/dx = x^2 * dt/dx - 2xt
稍整理,
(1 + x^2) dt/dx - 2xt = x
dt/dx - t * 2x/(1 + x^2) = x/(1 + x^2)
是個(gè)很標(biāo)準(zhǔn)的 First Order Ordinary Differential Equation.
相信從這里開(kāi)始你就會(huì)自己做了.