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Advanced Math Archive: Questions from October 02, 2022

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  4. Find the solution by using the method of variation of parameters (25\%) \[ y^{\prime \prime}-4 y^{\prime}+4 y=e^{2 x} \]
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  4. El histograma de la distribución correspondiente al peso de 100 alumnos de Bachillerato es el siguientes a) Construir la tabla de la distribución de datos agrupados b) Hallar la media y la desvia
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  Solve the following DE \[ y^{\prime}=\left(x^{2}+1\right) y \]
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  Solve the following DE \[ y^{\prime}=\left(x^{2}+1\right) y \]
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  a) \( \quad y^{\prime}=-\frac{x}{y} \) b) \( \frac{d y}{d x}=y^{2}-4 \) c) \( e^{x} y \frac{d y}{d x}=e^{-y}+e^{-2 x-y} \) d) \( y^{\prime}=y \) \( y^{\prime}+y=0 \) f) \( y^{\prime}+y=x \)
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  1. En el estudio se consideró la variable \( \mathrm{x} \), tiempo, en dias, que estuvieron en coma los pacientes que padecian una lesión craneal. Se recogieron los datos siguientes: \[ \begin{array
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  Proof if the following se's are convex. If not, provide a canterexarple. a) \( \left\{\left(x_{1}, x_{2}\right) \in \mathbb{R}^{2} \mid x_{2} \leq 3 ; x_{2} \geq-x_{1}, x_{2} \geq x_{1}\right\} \) b)
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  Solve: \[ \begin{array}{l} y^{\prime \prime}+11 y^{\prime \prime}+44 y^{\prime}+60 y=0 \\ y(0)=-2, y^{\prime}(0)=1, y^{\prime \prime}(0)=17 \\ y(t)= \end{array} \]
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  Solve: \[ \begin{array}{l} y^{(4)}+32 y^{\prime \prime}+256 y=0 \\ y(0)=-2, \quad y^{\prime}(0)=-18, y^{\prime \prime}(0)=24, y^{\prime \prime}(0)=352 \end{array} \]
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  Find the solution of the following initial value problems 1. \( y^{\prime \prime}+4 y=5 \sin (x), y(0)=y^{\prime}(0)=0 \) 2. \( y^{\prime \prime}+4 y=5 \sin (2 x), y(0)=y^{\prime}(0)=0 \). 3. \( y^{\
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  Identify the local extrema of \( f(x, y)=\left(x^{2}+y^{2}\right) e^{-y} \).
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• Evaluate the following integrals. Find the principal values if necessary:
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  3. Prove whether the following subsets of \( \mathbb{R}^{4} \) are vector subspaces. (a) \( V_{a}=\{(x, y, y, z) \mid x, y, z \in \mathbb{R}\} \) (b) \( V_{b}=\{(x, y, 0,0) \mid x, y \in \mathbb{R}\}
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• Use MATLAB to compute all derivatives and check that the indicated function is the particular solution of the differential equation. x3 y´´´+2x2y´´+20xy´-78y=0 y= 20cos⁡(5lnx)x-3(sen⁡(5lnx
  \( x^{3} y^{\prime \prime \prime}+2 x^{2} y^{\prime \prime}+20 x y^{\prime}-78 y=0 \) \( y=20 \frac{\cos (5 \ln x)}{x}-3 \frac{(\operatorname{sen}(5 \ln x)}{x} \) Comprobar que la función indicada es
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• Determine if the method of undetermined coefficients is applicable. Answer "yes" or "no".
  Determine si el método de coeficientes indeterminados es aplicable. Conteste "s' 0 "no". \[ \begin{array}{l} y^{\prime \prime}+4 y^{\prime}-5 y=x^{-2} e^{x} \\ y^{\prime \prime}+4 y^{\prime}-5 y=x^{2
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  Find the general solution to \[ y^{\prime \prime}-y^{\prime}-6 y=6 x^{3}+26 \sin 2 x \]
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  Solve \( y^{\prime}=(y-1)(y+2) x, \quad y(0)=9 \) \[ y(x)= \]
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  Evaluate the following integrals: (a) \( \int_{-\infty}^{\infty} \delta(\tau) x(t-\tau) d \tau \) (b) \( \int_{-\infty}^{\infty} x(\tau) \delta(t-\tau) d \tau \) (c) \( \int_{-\infty}^{\infty} \delta(
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• Determine which options are a solution of the differential equation.
  Determine cual o cuales de las siguientes funciones es (son) solución(es) de la ecuación diferencial \( x y^{\prime \prime}-y^{\prime}=0 \) a. \( y=0 \) b. \( \mathrm{y}=2 \) c. \( y=2 x \) d. \( y=
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• Determine which options are a solution for the differential equation.
  Determine cual o cuales de las siguientes funciones es (son) solución (es) de la ecuación diferencial \( y^{\prime \prime}-9 \mathrm{y}=18 \) a. \( y=0 \) b. \( y=2 \) c. \( y=2 x \) d. \( y=2 x^{2}
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• Homogeneous transformation matrices. Obtain the orientation transformation matrix of the system and the resulting vector of the output to align: (i) h on b and (ii) b on h.
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• homogeneous transformation matrices. If the origin point of the absolute and monitoring system is at O ​​(Ox, Oy, Oz) and the vehicle moves with its respective axes at position P(Px, Py, Pz), dete
  B. Si el punto origen del sistema absoluto y de monitoreo se encuentra en \( O\left(O_{x}, O_{r}, O_{2}\right) \) y el vehiculo se mueve con sus respectivos ejes en la posición \( \mathbf{P}\left(\ma
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