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求微分方程dy/dx=(4x+3Y)/(x+y)的通解
人气:313 ℃ 时间:2019-10-23 03:45:31
解答
dy/dx=(4x+3y)/(x+y)dy/dx=3+x/(x+y)y/x=u dy=udx+xduu+xdu/dx=3+1/(1+u)xdu/dx=3-u+1/(1+u)(1+u)du/(4+2u-u^2)=dx/x(-1+u)du/(4+2u-u^2)-2du/(4+2u-u^2)=dx/x(-1/2)dln(4+2u-u^2)-2du/[5-(u-1)^2]=dlnxdu/[√5-(u-1...
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