常微分方程求解,重赏![2xy+(x^2)y+(y立方)/3]dx +(x^2 +y^2)dy = 0[2xy+(x^2)y+(y_数学解答

常微分方程求解,重赏![2xy+(x^2)y+(y立方)/3]dx +(x^2 +y^2)dy = 0
[2xy+(x^2)y+(y立方)/3]dx +(x^2 +y^2)dy = 0

人气：288 ℃　时间：2020-01-09 12:02:21

解答

∵(2xy+x²y+y³/3)dx+(x²+y²)dy=0==>e^x*(2xy+x²y+y³/3)dx+e^x*(x²+y²)dy=0==>2xye^xdx+x²ye^xdx+y³e^x/3dx+x²e^xdy+y²e^xdy=0==>ye^xd(x²)+x...