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Advanced Math Archive: Questions from April 10, 2022

• Solve the following equations:
  (a) (20 pts) y' = 1 - sint - Sy(t)d7, con y(0) = 0 (b) (20 pts) - 27(0) = f(e- et-T)dt (c) (30 pts) y" + 3y = h(t) con h(t) = Scos(t - 4 0534 con y(0) = v'O) = 0
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• FIND ITS PARTIAL FRACTION DECOMPOSITION
  (-x4 – 17x3 – 13x2 + 173x – 169) (x - 2)(x2 + 3x – 7)2
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  2. Solve the initial value problems. a) y" + y = x, and y(0) = 1, y(0) = 0 b) y" + y = 8cos2x - 4sinx, y(t/2) = -1, y'(1/2) = -0
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  4) Solve the system da y, ma=0 = x, = dy = ī, ya=0 = y. da = - da Answer: m = x cosh a + y sinh a, y = x sinh a + y cosh a. 5) Calculate the exponential map for the Cauchy problem dx dt y, el=0 = x,
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• Find all the second partial derivatives. f(x, y) = x6y9 + 9x4y fxx(x, y) = fxy(x, y) = fyx(x, y) = fyy(x, y) =
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  2. (10.00 (tyli.com 1900-1) lv 0 su pon x + 2) ve la 1 ܫ ܀ ܙ ܀ ܙܘܢܘ 1 y su uso e manº s}
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• Please do d,e,g,h please
  Exercises = = = = = = 1. Use the Laplace transform to find the solution of the IVP. a) y' + 4y = 3H(t – 1), y(0) = 1 1 b) 2 - 4 =1 – HK1 – 4), g(0) = -1 c) y' + y = 28(t – 3), y(0) = -1 - d) y
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• Please help with d & h, thanks
  = - = - - 1. Use the Laplace transform to find the solution of the IVP. a) y' + 4y = 3H(t - 1), y(0) = -1 b) 3y' - y=1 - H(t - 4), y(0) = -1 c) y' + y = 28(t – 3), y(0) = -1 d) y' - 4y = 2H(t - 2) -
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  Solve each of the following d.e.'s (i) x²y" + 4 x y’ + 2 y = 0; (ii) xạy” + 4 x y' + 2 y = x; (iii) x²y” +4 x y' + 2 y =et.
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  Solve the d.e.y” - 9 y + 20 y = sin(x) - cos(x). Solve the d.e.y” - 9 y' + 20 y= eux.
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• using gauss-jordan method
  = 2. 2x - y = 10 - 3x + y = -15
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• can i please get help wirh these questions
  Problems 1-7: Use Laplace transforms to find th = = 1: y' - y = 1, y(0) = 1 2: y' + 7y = e3t, y(0) = 2 3: y" + 5y + 4y = 0, y(0) = 2, y'(0) = 0 4: y" + y = 3 sin V2t, y(0) = 0, y(0) = 5 5: y" + 2y' +
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• Consider the 5×5 system of equations given by: in the unknowns x1,x2,x3,x4,x5 (in that order they appear in the system). Then, the value of x1 that is part of the solution of this system is:
  Considere el sistema de ecuaciones 5 X 5 dado por 8 5 - 1 2 3 4 5 02 -1 0 0 0 3 -1 0 0 0 0 0 3 5 0 0 0 7 12 10 -12 -28 en las incógnitas X1, X2, X3, X4, X5 (en ese orden aparecen en el sistema). Ento
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• Find f ''(x). f(x) = 4x11 + 2x7 − x2 f ''(x) = Find y''. y = x2 ln(6x) y'' =
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• 18
  - In Problems 17-28, find two power series solutions of the given . differential equation about the ordinary point x = 0. 17. y" – 3xy = 0 18. y" + x²y = 0 19. y" - 2xy' + y = 0 20. y" – xy' + 2y
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• Resolver la integral donde C est´a determinado por |z| = 10. Solve the integral where C is determined by |z| = 10.
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