2ydx+(y^3-x)dy=0
dx/dy-(1/2y)x=-y^2/2,这是一阶线性方程,由通解公式:
e^∫(1/2y)dy=√y
x=√y(C+∫[(-y^2/2)/√y]dy)
=√y(C-(1/5)y^(5/2)
=C√y-(1/5)y^3
2ydx+(y^3-x)dy=0
dx/dy-(1/2y)x=-y^2/2,这是一阶线性方程,由通解公式:
e^∫(1/2y)dy=√y
x=√y(C+∫[(-y^2/2)/√y]dy)
=√y(C-(1/5)y^(5/2)
=C√y-(1/5)y^3