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,
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![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,](/uploads/image/z/9777877-61-7.jpg?t=%E6%B1%82%E8%A7%A3%E4%B8%80%E9%81%93%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E9%A2%98%26%238203%3Bx%2Ay%5E3%2Ady%2B%28y%5E4-x%5E2%29%2Adx%3D0%E5%A6%82%E9%A2%98+x%2Ay%5E3%2Ady%2B%28y%5E4-x%5E2%29%2Adx%3D0%E6%9C%80%E5%90%8E%E6%B2%A1%E8%83%BD%E7%94%A8d%28x%5E4%2Ay%29%E7%9A%84%E5%BD%A2%E5%BC%8F%E8%BF%9B%E8%A1%8C%E5%8C%96%E7%AE%80%2C%E7%BB%93%E6%9E%9C%E5%B0%B1%E5%81%9A%E4%B8%8D%E6%9D%A5%E4%BA%86%2C)
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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?