(xy^2-x)dx-(y+yx^2)dy=0,求这个微分方程的通解.

求方程(y^2+xy^2)dx+(x^2-yx^2)dy=0的通解 (xy^2-x)dx-(y+yx^2)dy=0,求这个微分方程的通解. 解微分方程y(x^2-xy+y^2)+x(x^2+xy+y^2)dy/dx=0答案yx=ce^[-arctan(y/x)] L为x^2+y^2=4,计算∮(x-yx^2)dx+(xy^2)dy的值? (x³-2xy²)dy+(2y³-3yx²)dx=0求通解 -x^2y+5xy^2-yx^2合并同类项 xy^2-x-yx^2+y变为(y-x)(xy+1)xy^2-x-yx^2+y化为(y-x)(xy+1)感觉不像十字相乘法. ∫C (yx^3+e^y)dx+(xy^3+xe^y-2y)dy,其中C为正向圆周x^2+y^2=a^2 求方程dy/dx=(1+y^2)/(xy+yx^3)的解. 一道常微分中变量可分离方程dy/dx=(1+y^2)/(xy+yx^3), 求 ∫L（-yx^2-2y）dx+（xy^2+x）dy L是逆时针方向的园x^2+y^2=a^2 求微分方程（y^2+xy^2)dx-(x^2+yx^2)dy=0,满足初始条件（y/x=1）=-1的特解 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 求dy/dx=x+xy^/y+yx^满足初始条件y｜(下面是x=0)=2的特解． 3xy+xy+2x²y+yx²+3x²y等于多少 xy-3xy+2yx-yx (xy-x^2)÷x^2-2xy+y^2/xy*x-y/y^2*yx^-2(xy-x^2)÷{x^2-2xy+y^2/xy}*{x-y/y^2}*{yx^-2} 因式分解x^2+xy+3x+3yx^2+xy+3x+3y 因式分解