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

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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
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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
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

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
∵(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)+x²yd(e^x)+y³/3d(e^x)+x²e^xdy+e^xd(y³/3)=0
==>yd(x²e^x)+x²e^xdy+d(y³e^x/3)=0
==>d(x²ye^x)+d(y³e^x/3)=0
∴x²ye^x+y³e^x/3=C （C是积分常数）
故原微分方程的通解是x²ye^x+y³e^x/3=C （C是积分常数）.

由原方程得：
2xydx+(x^2+y^2)dy+(x^2y+y^3/3)dx=0
左边两项为全微分
2xydx+(x^2+y^2)dy=d(x^2y+y^3/3)
于是有
d(x^2y+y^3/3)+(x^2y+y^3/3)dx=0
显然x^2y+y^3/3=0是一个特解
若x^2y+y^3/3 ≠0，则
ln|x^2y+y^3/3|+x=C
两解可统一写为
x^2y+y^3/3=Ce^(-x)

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 求解常微分方程 y+2xy'+(x^2)y''=0 坐等… 求解常微分方程!y'=xy-x^2+1,且y(0)=1.0 求解常微分方程 xy(y-xy')=x+yy',y（0）=（1/2）*根号2 求解一道常微分方程题dy/dx=(y^6-2x^2)/(2xy^5+x^2y^2) 求解常微分方程：x(x-1)y''-2xy'+2y=0用两边求导的方法怎么做? 常微分方程dy/dx=(x^3+xy^2)/y 求解常微分方程 y+2xy'+(x^2)y'' 坐等……呃，是y+2xy'+(x^2)y''=0 求解微分方程 x^2*dy/dx=xy-y^2 微分方程求解 (x^2y^3+xy)dy=dx 微分方程求解 (x^2y^3+xy)dy=dx xy''-y'-x^2=0求解微分方程 常微分方程求解：（1）1+y'=e^y (2)xy'+y=y^2 微分方程xy'=2y求解 求解微分方程xy''-y'+2=0, 常微分方程求解!y''+4xy'+(4x^2-2)y=0这个方程怎么解啊?我觉得应该设点什么?.但是. (x+2y)dx+(2x-3y)dy=0 求解常微分方程 求解常微分方程:y'+2x=根号下的(y+x^2)