• 2022-06-19
    把下列方程化为标准形式.[tex=5.286x1.286]jHgo9hRFCnGBzVWSOvgoUj81TlTopU3IiCoIwDXRO2g=[/tex]
  • 解:[tex=6.286x1.5]34izgKbaT/CIyb57RIu5whMF79sUC+ClpczRa7WV8iE=[/tex]①当x<0,则[tex=6.0x1.5]34izgKbaT/CIyb57RIu5wtTmqnpD/Yd8p8IXpxSDZko=[/tex],方程为双曲型[tex=11.143x2.571]CvyIkmwiTv5AMf6X0zLqUw/VjEktbz5lk72oPs0DoMgy+nADIg5Vn1XA4Y1W68Al6BPn2Rktqu4gBcIZy8ObxkwDnw65pqnzzgKNb0WmbdU=[/tex][tex=14.429x2.357]RS1baGYPw1gs3sAxwEFoEuOt9kKt62MvwBxpBHmykooeLTIAnTOrYYH4rUXqO+GEXx2GtNJfk+CyoGYexweFclL2PqGSanNAFnufkM637fY=[/tex],代入系数计算公式[tex=22.0x10.357]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[/tex]标准形式为[tex=14.429x2.786]Lb/kTWLvLTSd+Mp9n7g2zqCMd6W2WsWs+xiv1GsAMDy1fkZjCN75cZ0eCuLkEIizeQpIpoMdPxtD5Vq7wOOqsa1te1Sh4WA7gSgdfxcSTA4GMU75iBOdQmyV2xC0SilVPrAXr3IjLCdEWspG2iIksQ==[/tex].由[tex=7.571x2.429]lD90ISFDfgoNdncTfzerLxQOH59dZHDSgtMoKAJ5hBgK1m9E+6lqhfHbKjiIU6d9[/tex]代入标准形式化简即得[tex=10.429x2.643]ckYy+eNTEMSNzPvMPmDGHVAFxy1YCN7lcIYb7768qg8Fh6ziDaQn8O1ffPMQMZy0B/XnkFCBBnpuZjwWqEFM1lLarFfYJ2GOT11ScUdZDR8=[/tex].②当x>0,则[tex=6.0x1.5]34izgKbaT/CIyb57RIu5wqg8kXuIknqlHZtIkX28qa4=[/tex],方程为椭圆型,[tex=10.286x2.5]CvyIkmwiTv5AMf6X0zLqUw/VjEktbz5lk72oPs0DoMgy+nADIg5Vn1XA4Y1W68Alu7+awo9yvId4n+TwBzKUNxtZOf6sR+V9LwrmOCKCZPI=[/tex],令[tex=12.214x2.357]RS1baGYPw1gs3sAxwEFoEtewBrswsLhVWkqJjnUvqI064W0tk8Xgk7+oHUGu1w9lfDHS8UTUCAJnWCxa7xexBqDlYiDVnFseAVielphh+xE=[/tex],进一步又令[tex=15.929x2.357]VLdHjmITTnWRNrLNpodpYjbm4lCtPc2b5QjnTblx9EKwnhy2WbJvrhPhhTSLRxbZRSpRqAGr8yP8R2dbsNFR8mAjcA6+KprQyJzZD5/s1kAAphMO0rXbPK5EVw4eizo0[/tex].由系数公式得[tex=11.571x5.643]Ck4j1YFlvVH5wCAykOEMiyrmnqYNnmBgqmxT0UXmT8OsuS+VmFYKsd9gzSSPL2HkNrSVy66Lh3sND0jCTz54i/fsrz2QZ/Xro4BwKUAuRN7BLwMOTe1gBEVGjUcDRaMqbI5slpwHZQig9S6BD959dtt8anL3muxR6S4iZ2zARc60nDTZSbE3dZj6kLhu8cTSOIq0fKpbpFQ6xDEjK0tmww==[/tex],标准形式[tex=8.143x2.357]m11DmVK9SocZ9Ulr+Gg+5be/QU3JBQr+7ITyGT8CmO4T9ff2b+PiMHDlx5BgUxAy6c+8MZfPnwoH33VMGuumF51M9vYnMtK0zX0MG5geZPY=[/tex].将角标记号换为[tex=1.429x1.214]aFgGZFpUeVjcpHgNAHHQdg==[/tex],且[tex=3.786x1.5]L3GfokkxXVDsJplB/oMANOdp7d4hrBtprqr5Q6SoHkk=[/tex],即得[tex=7.786x2.571]KpOUnW5K+HmaIB1mKIdDZHik+PXVh5gOZTAq3d33/geYANjes7nl8dqqqUJgOP5YGUWozE9yOrExfGqJFa0oxg==[/tex]

    内容

    • 0

      验证函数满足拉普拉斯方程 [tex=5.286x1.286]GGdu5D2HECSRsnGkbWWW9ITikfXLJFnp8bT4IayUJdk=[/tex][tex=9.357x1.357]8edtLEcH2Vlg77PTHC5maDPGcDSavJa2tLWfTOcaNCJp+rW10Fo8kJOL67pLSjm4nwntVtgUbqimSrzRfnq7UQ==[/tex]

    • 1

      将下列直线的普通方程化为标准方程:[tex=4.857x2.786]fnpmC2J6JmQBLyo5NmGAz/eC7si1ymmDTCkcJm1MHie4aps/gLlBO0rIbiX+2XmDgvDbcgtrq14v3DjjKiOOiA==[/tex]。

    • 2

      验证函数满足拉普拉斯方程 [tex=5.286x1.286]GGdu5D2HECSRsnGkbWWW9ITikfXLJFnp8bT4IayUJdk=[/tex][tex=5.286x2.357]GZL8doY0d/PboQHLQlBV8M0bDoU4nsizA5jcDQaqhJU=[/tex]

    • 3

      根据提示,先把下列方程组化为标准的方程然后求出通解:[tex=11.5x1.571]ijk+2eXKRxevaYdpvp2E67D/RzNyP66NIqChVMZzYc35KYsTKnGfGIRTEsD/fDBQT4DT5WeoQSnpmKUYdf7ouHk81tszONx7jlQqCMWoMEI=[/tex](令z=λx).

    • 4

      设有方程 [tex=9.5x1.286]Ei2PZQl92La73hUrygebczy0hSgSKKIy9GY8YhdYHME8Vc+GOhh3ElB+8etaYJz3ndqY7VKsG0XTSjYLPzSgjbJWilgJb/61tuXaUj9FOiE=[/tex] 若把 [tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex] 看成因变量, [tex=0.5x1.0]yBR4oiFoTexGaFalQ7m8kg==[/tex] 看成自变量,则此方程化为何种形式?并求此方程的通解.