Question

dx/dy=x+y如何积分?

Answer 1

dx/dy=x+y

dx-(x+y)dy=0,(x+y)dy/dx=1

∵M=1,N=-(x+y),∂M/∂y=0,∂N/∂x=-1

[∂M/∂y-∂N/∂x]/M=+1

∴I=e^∫(-1)dy=e^(-y)

d[e^(-y)*(x+y)]=e^(-y)dy

e^(-y)*(x+y)=-e^(-y)+c

∴x+y=-1+c*e^y (c 是积分常数)

x = -1 - y + c*e^y

验证：dx/dy = - 1 + c*e^y

= x + y

∴【解答正确】