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Advanced Math Archive: Questions from March 17, 2023

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  Determine the domain of the function \[ f(x, y)=-\ln \left(3 x-2 y^{2}+3\right) \]
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  Solve the given initial-value problem. \[ y^{\prime \prime \prime}-2 y^{\prime \prime}+y^{\prime}=2-24 e^{x}+40 e^{5 x}, \quad y(0)=\frac{1}{2}, y^{\prime}(0)=\frac{5}{2} \] \[ y(x)= \]
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  (2) \( y^{\prime \prime}+4 y=8 \sin 2 x+12 \cos 2 x \)
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• Find particular solutions for the following nonhomogeneous ODEs. (a) y′′ − 3y′ + 2y = (1 + x)e^3x (b) y′′ + 2y′ + y = (2 + 3x)e^−x (c) y′′ + 2y′ + y = (6 cos(x) + 17 sin(x)) e^x
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  1. Find the solution to the initial value problem \[ \begin{aligned} y^{\prime \prime \prime}+y^{\prime \prime}-y^{\prime}-y & =0 \\ y(0) & =1, y^{\prime}(0)=-1, y^{\prime \prime}(0)=5 . \end{aligned}
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  Differentiate the function. \[ y=\frac{8 x^{2}-1}{2 x^{3}+5} \] Which of the following shows how to find the derivative of \( f(x) \) ? \( y^{\prime}=\frac{\left(8 x^{2}-1\right)\left(\frac{d}{d x}\le
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  The general solution to the DE \( y^{\prime}=\frac{1-x^{2}}{y^{2}} \) is None of these. \[ y=\left(3 x-x^{3}\right)^{1 / 3} \] \[ y=\left(3 x-x^{3}+c\right)^{1 / 3} \] \[ y=\left(3 x-x^{3}\right)^{1 /
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• Use an argument to prove
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• Find the intersection of these points:
  Intersección: \[ \begin{array}{c} T=f(x, y)=\frac{4}{900} x^{2}-0.04 y^{2}+18 \\ C=f(x, y)=-\left(0.006 x^{2}-0.006 y^{2}\right)+24 \end{array} \]
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• SOLVE IT BY THE UNDETERMINED COEFFICIENT METHOD
  \( -\frac{1}{4} y^{\prime \prime}+y^{\prime}+y=x^{2}-2 x \)
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• Mathematical Structures.
  B) For all \( x, y, z \in \mathbb{R}, \frac{x y}{z}=\left(\frac{x}{z}\right) y \) if \( z \neq 0, \frac{x}{y z}=\left(\frac{x}{y}\right) \frac{1}{z}=\frac{\left(\frac{x}{y}\right)}{z} \) if \( y, z \n
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• Please help solve #132, #133, and #138! Thank you!
  123. \( x^{2} y^{\prime}=(x+1) y \) 124. \( y^{\prime}=\tan (y) x \) 125. \( y^{\prime}=2 x y^{2} \) 126. \( \frac{d y}{d t}=y \cos (3 t+2) \) 127. \( 2 x \frac{d y}{d x}=y^{2} \) 128. \( y^{\prime}=e
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  Find the rate of change of \( y \) with respect to \( x \) for each of the following. (a) \( y=\frac{4 x+2}{x-1} \) (b) \( y=\frac{3 x-5}{6 x+2} \) (c) \( y=\frac{x^{2}+1}{2 x+5} \) (d) \( y=\frac{3 x
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  Differentiate the following functions with respect to \( x \). (a) \( y=(6 x+1)^{5} \) (b) \( y=(4-3 x)^{6} \) (c) \( y=\sqrt{2 x+9} \) (d) \( y=\frac{4}{\sqrt{5 x+1}} \) (e) \( y=\left(6 x^{2}+3 x+1\
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  III. Solve the following IVPs using Laplace Transform: 1. \( 4 y^{\prime \prime}-4 y^{\prime}-3 y=0 \quad y(0)=1, y^{\prime}(0)=5 \) 2. \( y^{\prime \prime}+4 y^{\prime}+5 y=35 e^{-4 x} \quad y(0)=-3,
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  In exercises 1-6, describe and sketch the domain of the function. 1. \( f(x, y)=\frac{1}{x+y} \) 2. \( f(x, y)=\frac{3 x y}{y-x^{2}} \) 3. \( f(x, y)=\ln \left(x^{2}+y^{2}-1\right) \) 4. \( f(x, y)=\f
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• Is this true or false? Explain if possible
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• Is this true or false? Explain if possible
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• Is this true or false? Explain if possible
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• Is this true or false? Explain if possible
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• Let U=(1,2,3,4,5,6,7,8), with the usual order. Find the binary vector corresponding to each of the following sets. A={2,4,8},B=(1,3,4,7,8],C=(5,6,7,8},D={1,2,3,4}. Using the binary vectors found, sear
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• Realiza la demostración físico-matemática y describe los argumentos de los que surge el teorema de Euler.
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• Paraboloide hiperbolico
  El techo del gimnasio del Campus Monterrey tiene la forma del paraboloide hiperbólico dado por la función \[ z=f(x, y)=0.25 x^{2}-0.1 y^{2}+15 \] Un trabajador de intendencia está haciendo mantenim
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  Solve the initial value problem \( y^{\prime \prime}+y^{\prime}+2 y=0, y(0)=y^{\prime}(0)=0 \)
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  Se tiene un vaso en forma de un cono truncado de radios \( r_{1}=3 \mathrm{~cm}, r_{2}=5 \mathrm{~cm} \) y altura \( \mathrm{h}=12 \mathrm{~cm} \), como el que se muestra en la figura siguiente, si se
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  Suponer que dejamos caer una bola esférica densa desde una gran altura en un planeta con atmósfera en donde la constante de la aceleración de la gravedad es \( g=13.25 \). Suponer que la resistenci
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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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• Find the intersection points
  \( \begin{array}{c}T=f(x, y)=\frac{4}{900} x^{2}-0.04 y^{2}+18 \\ C=f(x, y)=-\left(0.13 x^{2}+0.13 y^{2}\right)+24\end{array} \)
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• box the answer please
  Solve the given differential equation. \[ y^{(4)}+3 y^{\prime \prime \prime}-16 y^{\prime \prime}-48 y^{\prime}=0 \] \[ \begin{array}{l} \square y=C_{1}+C_{2} e^{4 x}+C_{3} e^{-4 x}+C_{4} e^{3 x} \\ y
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• Find the general solution of DE y′ + y tan x = sin(2x)
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• ​​​​​​​​​​​​​​
  4. (10 puntos) Usa una sustitución para convertir la integral a una integral de funciones racionales. Luego usa fracciones parciales para encontrar la integral. a. \( \int \frac{d x}{\sqrt{x}+3 x^{1
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• We will use the bisection method to find a root of the function. The root is known to lie between a = -2 and b = 2. Complete the table such that a < b, and c is the midpoint between a and b. At eac
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• The bisection method will be used to find a root of the function. It is known that the root lies between a = 2 and b = 4. f(x) = 2* sen(x) - 3x In(«2) + 15 Complete the table in such a way that
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  ¿Cómo es el polinomio que obtenemos de orden \( \mathrm{N} \) respecto al ajustado de \( \mathrm{N}+1 \) datos? Seleccione una: a. Único b. No se pueden utilizar parte de la aplicación previa c. G
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• odds only.
  In Exercises 25 through 29 , find for \( x=1 \) the \( y \) value for the particular solution required. 25. \( \left(D^{2}-2 D-3\right) y=0 \); when \( x=0, y=4, y^{\prime}=0 \) When \( x=1, y=e^{3}+3
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• solve the IVP
  \( y^{\prime}+y=u_{4}(t) t-\delta(t-10), y(0)=-2 \)
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