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dy/dx = 1/(x+y)
两边倒数
dx/dy = x+y
dx/dy - x = y
两边乘以 e^(-y)
e^(-y)[dx/dy - x] = ye^(-y)
d/dx ( x.e^(-y) = ye^(-y)
两边积分
x.e^(-y)
=∫ye^(-y) dy
=-∫yde^(-y)
分部积分∫udv =uv -∫vdu
=-ye^(-y) +∫e^(-y) dy
=-ye^(-y) -e^(-y) +C
整理方程
x=-y -1 +C.e^(y)
dy/dx = 1/(x+y)
得出通解：x=-y -1 +C.e^(y)
两边倒数
dx/dy = x+y
dx/dy - x = y
两边乘以 e^(-y)
e^(-y)[dx/dy - x] = ye^(-y)
d/dx ( x.e^(-y) = ye^(-y)
两边积分
x.e^(-y)
=∫ye^(-y) dy
=-∫yde^(-y)
分部积分∫udv =uv -∫vdu
=-ye^(-y) +∫e^(-y) dy
=-ye^(-y) -e^(-y) +C
整理方程
x=-y -1 +C.e^(y)
dy/dx = 1/(x+y)
得出通解：x=-y -1 +C.e^(y)
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