求方程[xcos(x+y)+sin(x+y)]dx+xcos(x+y)dy=0的通解,
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求方程[xcos(x+y)+sin(x+y)]dx+xcos(x+y)dy=0的通解,
∵[xcos(x+y)+sin(x+y)]dx+xcos(x+y)dy=0
==>xcos(x+y)dx+xcos(x+y)dy+sin(x+y)dx=0
==>xcos(x+y)(dx+dy)+sin(x+y)dx=0
==>xcos(x+y)d(x+y)+sin(x+y)dx=0
==>xd(sin(x+y))+sin(x+y)dx=0
==>d(xsin(x+y))=0
==>xsin(x+y)=C (C是积分常数)
∴原方程的通解是xsin(x+y)=C.
==>xcos(x+y)dx+xcos(x+y)dy+sin(x+y)dx=0
==>xcos(x+y)(dx+dy)+sin(x+y)dx=0
==>xcos(x+y)d(x+y)+sin(x+y)dx=0
==>xd(sin(x+y))+sin(x+y)dx=0
==>d(xsin(x+y))=0
==>xsin(x+y)=C (C是积分常数)
∴原方程的通解是xsin(x+y)=C.
求方程[xcos(x+y)+sin(x+y)]dx+xcos(x+y)dy=0的通解,
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