求一道微分方程,
问题描述：
求一道微分方程,
y'=（x+y）^3
这一类的题不是很懂,麻烦讲的详细些
答
设u=x+y,则dy/dx=du/dx-1代入原方程得du/dx-1=u³ ==>du/dx=u³+1==>du/(u³+1)=dx==>1/3[1/(u+1)+(2-u)/(u²-u+1)]du=dx==>2/3[2/(u+1)-(2u-1)/(u²-u+1)+3/(u²-u+1)]du=dx==>2/3[2/(u+1)...