(y^2-6x)dy+2ydx=0, dx/dy-3x/y=-y/2, 是x对y的一阶线性微分方程,则
x = e^(∫3dy/y)[∫(-y/2)e^(-∫3dy/y)dy+C]
= y^3[-∫dy/(2y^2)+C] = y^3[1/(2y)+C] = y^2/2+Cy^3.
(x-y^3)dy+ydx=0 (y>0), dx/dy+x/y=y^2, 是x对y的一阶线性微分方程,则
x = e^(-∫dy/y)[∫y^2*e^(∫dy/y)dy+C]
= (1/y)[∫y^3dy+C] = (1/y)[y^4/4+C] = y^3/4+C/y.
构造全微分方程。