解微分方程 dy+(y-(y^2)*cosx+(y^2)*sinx)dx=0

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解微分方程 dy+(y-(y^2)*cosx+(y^2)*sinx)dx=0
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解微分方程 dy+(y-(y^2)*cosx+(y^2)*sinx)dx=0
解微分方程 dy+(y-(y^2)*cosx+(y^2)*sinx)dx=0

解微分方程 dy+(y-(y^2)*cosx+(y^2)*sinx)dx=0
dy+(y-(y^2)*cosx+(y^2)*sinx)dx=0
y'+y-(y^2)*cosx+(y^2)*sinx=0
-y'/y^2=1/y-cosx+sinx
设z=1/y代入:z'=z-cosx+sinx
z'=z的通z=Ce^x 令特解y=Asinx+Bcosx代入z'=z-cosx+sinx求得A=-1 B=0
通1/y=z=Ce^x-sinx