求解一道微分方程题​x*y^3*dy+(y^4-x^2)*dx=0如题 x*y^3*dy+(y^4-x^2)*dx=0最后没能用d(x^4*y)的形式进行化简,结果就做不来了,

求解一道微分方程题​x*y^3*dy+(y^4-x^2)*dx=0如题 x*y^3*dy+(y^4-x^2)*dx=0最后没能用d(x^4*y)的形式进行化简,结果就做不来了,
求解一道微分方程题​x*y^3*dy+(y^4-x^2)*dx=0
如题 x*y^3*dy+(y^4-x^2)*dx=0
最后没能用d(x^4*y)的形式进行化简,结果就做不来了,

求解一道微分方程题​x*y^3*dy+(y^4-x^2)*dx=0如题 x*y^3*dy+(y^4-x^2)*dx=0最后没能用d(x^4*y)的形式进行化简,结果就做不来了,
x*y^3*dy+(y^4-x^2)*dx=0
x*y^3*dy/dx+y^4-x^2=0
令 y=u/x
dy/dx=du/dx*1/x-u/x^2
x*(u/x)^3*(du/dx*1/x-u/x^2)+(u/x)^4-x^2=0
(u/x)^3*du/dx=x^2
u^3*du/dx=x^5
两边取不定积分
u^4/4=x^6/6+C
(xy)^4=x^6/6+C

http://www.wolframalpha.com/input/?i=x*y%5E3*dy%2B%28y%5E4-x%5E2%29*dx%3D0
能否有帮助？