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Advanced Math Archive: Questions from April 11, 2022

• Solve the following PDE (z^2-2yz-y^2)p+x(y+z)q=x(y-z)
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  Derive the two-dimensional sphere metric: ds2 = (a2 + sin? 0do2)
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  y > x + 1 Graph: 1 y< - x - 1 - y < 글 · 5 4 3 2 1 1 2 3 4 5 -5 -4 -3 -2 -2 -1 - 1 -2 -3 -4 -5 Clear All Draw:
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  3. (25 pts) Solve the following DE's a) y" – y' - 2y = 0 c) ylv - 2y + y = 0 b) y' + y" – y' - y = 0); d) yº + 2y'"' + y' = 0 ' yOh 2y(2x2 + Iny)dx - xdy = 0 - 4. (15 pts) Solve the DE
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• Both #19's are different problems. Do both for a like
  - 2s – 1 19. S-1 18-(s + 13) . In Problems 21-30 use the Laplace transform to solve the given initial-value problem. 21. y' + 4y = e-41, y(0) = 2 9 22. y' - y = 1 + te', y(0) = 0 23. y" + 2y' + y
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  Find the gradient vector field Vf of f. f(x, ) = (x - y)2 (x, y Vf(x, y) =
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  Problem 1. Solve y" + y = 48(t - 27), y(0) = 0, y' (O) = 0. Problem 2. Solve X'= -x + y y = 2.c (0) = 0, y(0) = 1.
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  2. Solve the initial-value problem y' = = tan (x) (1 + y2) y(0) = 1
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• Consider the function f(x) = 2x° -6x? to determine the following. one. Intervals for which the graph of f(x) is increasing or decreasing and the extremes relative. [Write the entire procedure] ..f(x)
  Nombre: Fecha: Número de estudiante: MECU 3032, Sección: TAREA PARA ENTREGAR #3 Valor: 20 puntos Considera la función /(x) = 2x - 6x para determinar lo que se indica a continuación a 1. Intervalos
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• Explain whether the following first-order differential equation can be solved using a substitution, and if so, solve it: Please use Bernoulli DE to resolve if its posible and explain step by step..Tha
  Situación: Explique si la siguiente ecuación diferencial de primer orden se puede resolver usando una sustitución y si es posible resuelvala: dy 3x + 2y 3x + 2y - 1 dx Se puede utilizar uno de los
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