Question

微分方程y′-3xy-xy^2=0的通解

Answer 1

y′-3xy-xy^2=0

dy/dx=x(3y+y²)

1/(3y+y²)dy=xdx

1/3【1/y-1/(y+3)】dy=xdx

1/3(lny-ln(y+3))=x²/2+lnc

1/3lny/(y+3)=lnce^(x²/2)

y/(y+3)=ce^(3x²/2)