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求微积分方程dy/dx=1/(x-y)的通解 5
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解:∵dy/dx=1/(x-y)
==>(x-y)dy=dx
==>信局喊dx-xdy=-ydy
==>e^(-y)dx-xe^(-y)dy=-ye^(-y)dy (等式两滑野端同乘e^(-y))
==>腊胡d(xe^(-y))=d((y+1)e^(-y))
==>xe^(-y)=(y+1)e^(-y)+C (C是常数)
==>x=y+1+Ce^y
∴原方程的通解是x=y+1+Ce^y。
==>(x-y)dy=dx
==>信局喊dx-xdy=-ydy
==>e^(-y)dx-xe^(-y)dy=-ye^(-y)dy (等式两滑野端同乘e^(-y))
==>腊胡d(xe^(-y))=d((y+1)e^(-y))
==>xe^(-y)=(y+1)e^(-y)+C (C是常数)
==>x=y+1+Ce^y
∴原方程的通解是x=y+1+Ce^y。
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