Advanced Math Archive: Questions from June 05, 2022
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solve any 4
1. Use variation of parameters to find the general solutions of the following equations a. y"-y'-2y = e²x b. y" + y = cos x c. y" + 4y = 4 sin²x d. y" + y = tan x e. y" + 2y' + y = xex f. y"-3y + 2y2 answers -
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Using the Frenet's equation definition find the Frenet's system (T, N, B, k, \tau) for the following curves:
Según la definición de las ecuaciones de Frenet, encuentre el sistema de Frenet (T, N, B, Ê, 7) para las curvas: a(t) = (sen(t), 2 cos(t), 1) a(t) = (t sen(t), t cos(t), 0) a(t) = (R sen(t), R cos(1 answer -
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(4.) Transform the following IVPS into algebraic equations and solve for L(y): (a) y' + 3y = t², y(0) = -1; (b) y" + y = sin 4t, y(0) = 0, y' (0) = 1; (c) y' + y = et sin 3t, y(0) = 0.1 answer -
Graph the following functions.
a. y(t) =t+it² para t € [−2,3] b. y(t) = 3eit + 5 − 4i para t € [0,2π]1 answer -
1. El campo de velocidad de un fluido está dado por F(x, y, z) = 5z ky sea S la esfera x² + y² + z²2 = 16. Calcule el flujo de F a través de S1 answer -
2. 2. Si F(x, y, z) = x²yi+y²j+xz k y S es el cubo del primer octante limitado por los planos x = 1 y = 1 yz = 1 y los planos coordenados. Calcule el flujo de F a través de S1 answer -
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Question 3 Find the explicit solution of the differential equation y = ± √√√ Aex² +6x +9 y = ± √√Aex +9 y = ± √√ Ae*² +6x+9 y = ± Aex² +9 y x + 3 -y' =y²-9. Question 4 Solve the1 answer -
Solve the partial differential equation for heat subject to the given conditions example:
4 (0,T) = 0 21 (L₁T) =O f(x) = x-x² u (x,0) = f(x) P = IT bn = 2 = [ { " f(x)sen (18x) dx)] = = [ S* ^ (nx-x²) sen(nx) dx] bn = 3 [~ √²xsen(nx) dx - √" x ²sen (nx)dx] 2 П bn = = ["[ - = x c1 answer -
7. Una barra uniforme está sujeta en x = 0 y está inicialmente en reposo. Si se aplica una fuerza constante F, al extremo libre en x = L, el desplazamiento longitudinal u(x, t) de una sección trans1 answer