解方程:dy/dx=y/x+tan(y/x)

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解方程:dy/dx=y/x+tan(y/x)解方程:dy/dx=y/x+tan(y/x)解方程:dy/dx=y/x+tan(y/x)令y/x=udu=d(y/x)=(xdy-ydx)/x则dy/dx=

解方程:dy/dx=y/x+tan(y/x)
解方程:dy/dx=y/x+tan(y/x)

解方程:dy/dx=y/x+tan(y/x)
令y/x = u
du = d(y/x) = (xdy-ydx)/x
则dy/dx = (x du/dx + y)/x = xdu/dx + u
代入原式代换
xdu/dx + u = u + tanu
cosudu/sinu = dx/x
积分得
ln|sinu| = ln|x| + C
即sinu = kx,或写作sin(y/x) = kx