Advanced Math Archive: Questions from June 05, 2023
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Considerando el atractor de Roosler, a) Resuclva el sistema: \[ \begin{array}{l} x^{\prime}=-y-z \\ y^{\prime}=x+a y \\ z^{\prime}=b+z(x-c) \end{array} \] considerando: \( \mathrm{a}=0.2, \mathrm{~b}=2 answers -
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Using the following properties of a twice-differentiable function \( y=f(x) \), select a possible graph of \( f \). Select one:2 answers -
Exercise 1 Solve the following separable variable differential equations: \[ \begin{array}{l} y^{\prime}=y \cdot \operatorname{tg} x, y=y(x) \\ y^{\prime}=y^{2} \cdot \operatorname{tg}^{2} x, y=y(x) \2 answers -
Exercise 2 Solve the following separable variable differential equations: \[ \begin{array}{l} \left(y^{2}+x y^{2}\right) d x+\left(x^{2}-y x^{2}\right) d y=0, y=y(x) \\ x y\left(1+x^{2}\right) d y-\le2 answers -
Exercise 3 solve the following separable variable differential equations: \[ \begin{array}{l} y^{\prime} \cdot \cos ^{2} x \cdot \operatorname{ctg} y+\operatorname{tg} x \cdot \sin ^{2} y=0, y=y(x) \\2 answers -
Exercise 4 Solve the following homogenuous differential equations: \[ \begin{array}{l} x \cdot y^{\prime}=y-x, y=y(x) ; \\ x \cdot y^{\prime}=-(y+x), y=y(x) ; \\ x^{2} \cdot y^{\prime}=y(x-y), y=y(x)2 answers -
Exercise 5 Solve the following homogenuous differential equations: \[ \begin{array}{l} y^{\prime}=\frac{2 x-y}{x+2 y}, y=y(x) \\ (2 x+y)-(4 x-y) y^{\prime}=0, y=y(x) \\ y^{\prime}=\frac{x+y}{x-y}, y=y2 answers -
\( y^{\prime}=\frac{1-2 x}{x^{2}} y=1, y=y(x) \) \( \begin{array}{l}y^{\prime}+2 x y=2 x e^{-x^{2}}, y=y(x) ; \\ y^{\prime}+\frac{3}{x} y=\frac{e^{2 x-1}}{x^{3}}, y=y(x) ; \\ y^{\prime}+2 x y+x-e^{-x^2 answers -
(b) (sin (30)+1/2) (sin (0) - 1) = 0 ) 0E(0,pie)
(b) \( \left(\sin (3 \theta)+\frac{1}{2}\right)(\sin (\theta)-1)=0 \)0 answers -
Tomar el examen Dado el sistema x+2y+4z=6 y+2z =4 x+3y+2z=1 Efectuar la reducción de Gauss-Jordan a) Nombre del sistema resultante Nota: Escribir, CONSISTENTE INDEPENDIENTE, CONSISTE DEPENDIENTE, INC
Dado el sistema \[ \begin{array}{r} x+2 y+4 z=6 \\ y+2 z=4 \\ x+3 y+2 z=1 \end{array} \] Efectuar la reducción de Gauss-Jordan a) Nombre del sistema resultante Nota: Escribir, CONSISTENTE INDEPENDIEN2 answers -
- 1. Utilice el teorema de Stokes para evaluar la integral de línea, donde \( \mathbf{F}(x, y, z)=\left(x+y^{2}\right) \mathbf{i}+\left(y+z^{2}\right) \mathbf{j}+\left(z+x^{2}\right) \mathbf{k} \) y2 answers -
find the principal inverse matrix
Encuentre la matriz inversa de la matriz principal del siguiente sistema de ecuaciones: \[ \begin{array}{l} x_{1}-3 x_{2}-x_{3}=2 \\ 3 x_{1}-x_{2}+2 x_{3}+x_{4}=13 \\ 3 x_{1}-2 x_{2}-x_{3}+2 x_{4}=252 answers -
Se da una región \( R \) en el plano \( x y \). Determine ecuaciones para una transformación \( T \) que convierta una región rectangular \( S \) en el plano uv en \( R \), donde los lados de \( S2 answers -
Find linearization of \( f(x, y)=\sqrt{x^{2}+y^{2}} \) at the point \( P(3,-4) \). Choose the correct answer. \[ \begin{array}{l} L(x, y)=\frac{3}{5} x-\frac{4}{5} y+4 \\ L(x, y)=3 x-4 y+4 \\ L(x, y)=2 answers -
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