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数学
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(x+y)^2 dy/dx=1做变换t=x+y后,求得通解为
人气:157 ℃ 时间:2020-05-22 02:00:23
解答
t=x+ydt/dx=1+dy/dxdy/dx=dt/dx-1t^2(dt/dx -1)=1dt/dx -1=1/t^2dt/dx=1/t^2+1=(t^2+1)/t^2t^2dt/(t^2+1)=dxdt-dt/(t^2+1)=dxt-arctant =x+Cx+y-arctan(x+y)=x+Cy-arctan(x+y)-C=0
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