刚学积分,帮忙求一道一元微分方程.
问题描述：
刚学积分,帮忙求一道一元微分方程.
y'=(y^2 - 2xy - x^2)/(y^2 + 2xy - x^2) 求它的解.
答
令y=xu则y'=u+xu'代入原方程得：u+xu'=(u^2-2u-1)/(u^2+2u-1)xu'=(u^2-2u-1)/(u^2+2u-1)-uxdu/dx=-(u+1+u^3+u^2)/(u^2+2u-1)du*(u^2+2u-1)/(u^3+u^2+u+1)=-dx/xdu*(u^2+2u-1)/[(u+1)(u^2+1)]=-dx/xdu*[ -1/(u+1)+2u/...