问题描述: 求dy/dx=x+xy^/y+yx^满足初始条件y|(下面是x=0) =2的特解.^是2,2次方 1个回答 分类:数学 2014-11-17 问题解答: 我来补答 dy/dx = (x+xy²)/(y+yx²)(y+yx²)dy = (x+xy²)dxydy + yx²dy - xdx - xy²dx = 0ydy - xdx + 1/2 * (x²dy² - y²dx²) = 0dy² - dx² + x²dy² - y²dx² = 0(1+x²)dy² = (1+y²)dx²dy²/(1+y²) = dx²/(1+x²)ln(1+y²) = ln(1+x²) + Cx=0时y=2则ln5 = C所求特解为ln(1+y²) = ln(1+x²) + ln5即y = √(4+5x²) 展开全文阅读