(A) Transform the following equation (1+x²)uz + uly = u into the canonical form and solve it. Find the solution under the initial con- dition u(0, y) = e³. (B) For the equation yurz – x²uxy + x²uyy + u+sin a = 0, describe the regions in the xy-plane where the equation is hyperbolic, parabolic or elliptic. Sketch the xy-plane and label where the equation is hyperbolic, where it is elliptic. and where it is parabolic.

Q: 4. (a) Suppose a pair of axes x and y is rotated by a to obtain a new pair of axes, X and Y. Show…

A:

Q: Verify that U(x,y) = x3y - xy3 is harmonic on the complex plane.

A:

Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1 – j2), j 2- j3 1 +…

A:

Q: 6. Consider F (w), a complex function of a real variable w: F (w) = (2+jw)/(3+j4w) a. Express F (w)…

A: Given: The complex function of a real variable .a) To express  in cartesian form and find it's real…

Q: What is the smallest number that can be represented as the sum of four positive squares (not…

A: Consider the given statement. Since we need to find a number, which is the smallest number of sum of…

Q: #1. show that wx, y) = x² + 2xy - y² + 2x +34 is harmonic in the compler plane. Find a harhonic…

A:

Q: ) Find a trig. identity that will help you eliminate t. This will be one-half of a familiar conic,…

A: In the given equation, the concept of a trigonometric function is applied. Trigonometric Functions…

Q: The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = parametric equations…

A: Given that the position vector of the point is P0 (x0, y0, z0) and parallel to the vector v = (v1,…

Q: Use, 0 = 60°, to write the rotated conic section given below, in the x'y'-plane. x² - y² = 9 Select…

A: