常微分方程（吉林大学） CAD2

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13£¶w«'4òÑ1ÙÐÈ©{§2;;;...§§§))){{{2.6T§Ä¤©/ª©§M(x,y)dx+N(x,y)dy=0.(2.20)¯ÌIKJJIIJI12
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13=U(x,y)=M(x,y),U(x,y)=N(x,y),(2.21)£xyK¡(2.20)T§,½©§.¶w«'4òÑe§(2.20)´T§,3¼êU(x,y),¦dU(x,y)=M(x,y)dx+N(x,y)dy≡0.¯ÌIKJJIIJI13
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3、e§(2.20)´T§,3¼êU(x,y),¦dU(x,y)=M(x,y)dx+N(x,y)dy≡0.u´U(x,y)≡CÒ´§(2.20)ÛªÏ),ùpC´?¿~ê.¯ÌIKJJIIJI13
13£¶w«'4òÑe§(2.20)´T§,3¼êU(x,y),¦dU(x,y)=M(x,y)dx+N(x,y)dy≡0.u´U(x,y)≡CÒ´§(2.20)ÛªÏ),ùpC´?¿~ê.ù,·g,JÑXe¯K:¯ÌIKJJIIJI13
13£¶w«'4òÑe§(2.20)´T§,3¼êU(x,y),¦dU(x,y)=M

4、(x,y)dx+N(x,y)dy≡0.u´U(x,y)≡CÒ´§(2.20)ÛªÏ),ùpC´?¿~ê.ù,·g,JÑXe¯K:¯Ì(1)XÛ½§(2.20)´T§?IKJJIIJI13
13£¶w«'4òÑe§(2.20)´T§,3¼êU(x,y),¦dU(x,y)=M(x,y)dx+N(x,y)dy≡0.u´U(x,y)≡CÒ´§(2.20)ÛªÏ),ùpC´?¿~ê.ù,·g,JÑXe¯K:¯Ì(1)XÛ½§(2.20)´T§?IK(2)XJ(2.20)´T§,XÛ¦¼êU(x,y)?JJIIJI13

5、
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6、)þuÝ/G:a

7、(x,y).òÑlMy(x,y)≡Uxy(x,y),Nx(x,y)≡Uyx(x,y).¯ÌIKJJIIJI15
13£¶w«'4òÑlMy(x,y)≡Uxy(x,y),Nx(x,y)≡Uyx(x,y).d®,My(x,y)ÚNx(x,y)ëY,Uxy(x,y)=Uyx(x,y),lMy(x,y)=Nx(x,y),=(2.22)¤á.¯ÌIKJJIIJI15
13£¶w«'4òÑlMy(x,y)≡Uxy(x,y),Nx(x,y)≡Uyx(x,y).d®,My(x,y)ÚNx(x,y)ëY,Uxy(x,y)=Uyx(x,y),l

8、My(x,y)=Nx(x,y),=(2.22)¤á.2y¿©5,=l(2.22)¤áíyd(2.23)½(2.24)¤LѼêU(x,y)÷v(2.21).¯ÌIKJJIIJI15
13£¶w«'4òÑlMy(x,y)≡Uxy(x