题目

(x+y)^2 dy/dx=1做变换t=x+y后,求得通解为

提问时间：2021-03-07

答案

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