求微分方程通解：dy/dx=(x-y+1)/(x+y^2+3)

求微分方程通解：dy/dx=(x-y+1)/(x+y^2+3)
求微分方程通解：dy/dx=(x-y+1)/(x+y^2+3)

求微分方程通解：dy/dx=(x-y+1)/(x+y^2+3)
(x+y^2+3)dy=(x-y+1)dx
或：xdy+ydx+(y^2+3)dy-(x+1)dx=
d(xy)+(y^2+3)dy-(x+1)dx=0
通解为：xy+y^3/3+3y-x^2/2-x=C

直接积分；
dy/dx=(x-y+1)/(x+y²+3) → (x+y²+3)dy=(x-y+1)dx；
两边积分：∫xdy+∫(y²+3)dy=∫(x+1)dx-∫ydx → xy-∫ydx+(y³/3)+3y=(x²/2)+x-∫ydx
→ xy+(y³/3)+3y=(x²/2)+x+C；