xy(dy/dx)=x^2+3y^2
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亲亲~十分感谢您的耐心等待,xydy/dx=x^2+3y^2xydy=x^2dx+3y^2dxxdy^2=2x^2dx+2y^2dxy^2=uxdy^2=udx+xdux(udx+xdu)=2x^2dx+2uxdxudx+xdu=2xdx+2udxxdu-udx=2xdxdu/x-udx/x^2=2dx/xd(u/x)=2dlnxu/x=C+2lnxu=Cx+2xlnxy^2/x=Cx+2xlnx通解y^2=Cx^2+2x^2lnxy|x=e =2e4e^2=C4e^2+8e^2C= -1特解y^2=2x^2lnx-x^2
咨询记录 · 回答于2022-11-15
xy(dy/dx)=x^2+3y^2
亲亲~十分感谢您的耐心等待,xydy/dx=x^2+3y^2xydy=x^2dx+3y^2dxxdy^2=2x^2dx+2y^2dxy^2=uxdy^2=udx+xdux(udx+xdu)=2x^2dx+2uxdxudx+xdu=2xdx+2udxxdu-udx=2xdxdu/x-udx/x^2=2dx/xd(u/x)=2dlnxu/x=C+2lnxu=Cx+2xlnxy^2/x=Cx+2xlnx通解y^2=Cx^2+2x^2lnxy|x=e =2e4e^2=C4e^2+8e^2C= -1特解y^2=2x^2lnx-x^2
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