dy/dx=1-cos(y-x)

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dy/dx=1-cos(y-x)dy/dx=1-cos(y-x)dy/dx=1-cos(y-x)换元u=y-x,则dy/dx=du/dx+1,原方程化为du/dx=-cosu,分离变量du/cosu=

dy/dx=1-cos(y-x)
dy/dx=1-cos(y-x)

dy/dx=1-cos(y-x)
换元u=y-x,则dy/dx=du/dx+1,原方程化为du/dx=-cosu,分离变量du/cosu=-dx,两边积分ln(secu+tanu)=-lnx+lnC,所以x(secu+tanu)=C,代入u=y-x得通解x(sec(y-x)+tan(y-x))=C