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Advanced Math Archive: Questions from March 20, 2023

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  the DE: \( \quad y^{\prime} \cos y-\frac{\sin y}{1+x}=(1+x) e^{x} \) 5. Solve the IVP: \( 4 y^{\prime}+17 y=0, \quad y(0)=-1, y^{\prime}(0)=2 \) 6. Solve the BVP: \( \quad\left(x^{2}+y^{2}\right) y^{\
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  Suponer que la población de una ciudad satisface la hipótesis exponencial: "La razón de cambio de la población en cualquier momento es proporcional a la población en ese momento." Tenemos los sig
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• g. y′′ − 6y′ + 9y = 0, y(0) = −2, y′(0) = 3 h. y′′ −2y′ +y = 0,y(0) = 3, y′(0) = −2 i. y′′ − 2y + 4y = 0,y(0) = 1,y′(0) = 2 j. y′′ +2y′ +5y = 0,y(0) = 2,y′(0) =
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• determine the limit in case it does not exist explain
  I. Determine el límite, en caso de que no exista explique por qué. a) \( \lim _{(x, y) \rightarrow(0,1)} \frac{\arccos (x / y)}{1+x y} \) b) \( \lim _{(x, y) \rightarrow(0,0)} \frac{x-y}{\sqrt{x}+\s
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• Find the solution u(x,y) of Laplace's equation in the rectangle 0 < 2 < 1,0 < y < 1 that also satisfies the boundary conditions.
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• Set up and solve the Boundary Value Problem (B.V.P.) for the steady-state temperature of a thin rectangular plate that coincides with the region defined by 0 ≤ a ≤ 4, 0 < y ‹ 2. The left end
  17. Establezca y resuelva el Problema de Valores en la Frontera (P.V.F.) para la temperatura de estado estable de una placa rectangular delgada que coincide con la región definida por \( 0 \leq x \le
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• I. Derermine the lenght of the arc in the given interval. II. Determine and interpret the curvature K of the curve at the value of the given parameter.
  I. Determine la longitud del arco en el intervalo dado a) \( r(t)=i+t^{2} j+t^{3} k ;[0,2] \) b) \( r(t)=\langle 4 t,-\cos t, \operatorname{sen} t\rangle ;\left[0, \frac{3 \pi}{2}\right] \) II. Determ
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  Evaluate the triple integral \( \iiint_{B} f(x, y, z) d V \) over the solid \( B \). \[ f(x, y, z)=1-\sqrt{x^{2}+y^{2}+z^{2}}, B=\left\{(x, y, z) \mid x^{2}+y^{2}+z^{2} \leq 25, y \geq 0, z \geq 0\rig
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  suelve \( y \frac{d x}{d y}=x+4 y e^{-2 x y} \) \[ \frac{1}{2} e^{2 x y}=\ln \mid y+c \] \( 2 e^{2 x y}=8 \ln |y|+c \) \( e^{2 x y}=8 \ln \mid y+c \) \( 4 e^{2 x y}=2 \ln |y|+c \) Ninguna de las anter
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  suelve \( \left(y+x \cot \frac{y}{x}\right) d x-x d y=0 \) \( \ln \cos \frac{y}{x}|=\ln | x \mid+c \) \[ x \cos \frac{y}{x}=c \] \[ \ln |x|=\sec ^{2}\left(\frac{y}{x}\right)+c \] Ninguna de las anteri
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• 3,9,15 show work
  In Problems 1 through 20, find a particular solution \( y_{p} \) of the given equation. In all these problems, primes denote derivatives with respect to \( x \). 1. \( y^{\prime \prime}+16 y=e^{3 x} \
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• 33, 39
  Solve the initial value problems in Problems 31 through 40. 31. \( y^{\prime \prime}+4 y=2 x ; y(0)=1, y^{\prime}(0)=2 \) 32. \( y^{\prime \prime}+3 y^{\prime}+2 y=e^{x} ; y(0)=0, y^{\prime}(0)=3 \) 3
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• 47, 53
  In Problems 47 through 56 , use the method of variation of parameters to find a particular solution of the given differential equation. 47. \( y^{\prime \prime}+3 y^{\prime}+2 y=4 e^{x} \) 48. \( y^{\
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• l. Find the total differential ll. Consider the function... a) Evaluate b) Calculate c) use the total differential dz to approximate z
  I. Halle el diferencial total a) \( z=e^{x} \operatorname{sen}(y) \) b) \( w=\frac{x+y}{z-3 y} \) II. Considere la función \( f(x, y)=y e^{x} \) y trabaje: a) Evaluar \( f(2,1) \) y \( f(2.1,1.05) \)
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• Solve the given initial-value problem. y'' + y' + 4y = 0, y(0) = y'(0) = 0
  4 answers