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  • Pregunta: 4.6 Exercises 1. Determine the region in which the given equation is hyperbolic, parabolic, or elliptic, and transform the equation in the respective region to canon- ical form. (a) xuxx + Uyy = 22, (b) uzx + yuyy = y; (c) Uzx + xyuyy = 0, (d) x?Uxx - 2xyuxy + y uyy = e", (e) Upx + xy - xuyy = 0, (f) e' uxx + euyy = u, Vyuxy + () uyy + 2x Uz – 3y uy + 2u =


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    Paso 1

    (a)XUXX+UYY=X2

    here a = the coefficent of Uxx = X , b= coefficent of Uxy =0

    and c= the coefficient of Uyy= 1.

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Texto de la transcripción de la imagen:
4.6 Exercises 1. Determine the region in which the given equation is hyperbolic, parabolic, or elliptic, and transform the equation in the respective region to canon- ical form. (a) xuxx + Uyy = 22, (b) uzx + yuyy = y; (c) Uzx + xyuyy = 0, (d) x?Uxx - 2xyuxy + y uyy = e", (e) Upx + xy - xuyy = 0, (f) e' uxx + euyy = u, Vyuxy + () uyy + 2x Uz – 3y uy + 2u = exp (22 – 2y), y > 0 Výuay + xuyy = cos (22 – 2y), y20, (h) un Uxx - yuxy + xux + yuy + u = 0, (j) sin² x Uxx + sin 2x Uxy + cos² x Uyy = x,