Advanced Math Archive: Questions from April 05, 2023
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3. Solve the initial-value problem: \[ y^{\prime \prime}-6 y^{\prime}+9 y=18 \cos (3 x), \quad y(0)=1, \quad y^{\prime}(0)=0 \]2 answers -
Which system is the only inconsistent system? \[ \begin{array}{l} y=x-3 \\ y=3 x-1 \\ y=3 x-2 \\ 2 y=6 x-4 \\ y=x-3 \\ y=-x-1 \\ y=3 x-6 \\ y=3 x+6 \end{array} \]2 answers -
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Number 204. please
In the following exercises, evaluate the triple integrals over the bounded region \[ E=\left\{(x, y, z) \mid g_{1}(y) \leq x \leq g_{2}(y), c \leq y \leq d, u_{1}(x, y) \leq z \leq u_{2}(x, y)\right\}2 answers -
differential equations
3) Solve the I.V.P: a) \( y^{\prime \prime}+2 y^{\prime}+y=0 ; y(0)=1, y^{\prime}(0)=-3 \) b) \( y^{\prime \prime}-2 y^{\prime}+2 y=0 ; y(0)=0, y^{\prime}(0)=2 \)2 answers -
Solve in details the answer will be:
67. \( y^{\prime \prime}+4 y=\sin t \vartheta(t-2 \pi), \quad y(0)=1, \quad y^{\prime}(0)=0 \) \( y=\cos 2 t+\left[\frac{1}{3} \sin (t-2 \pi)-\frac{1}{6} \sin 2(t-2 \pi)\right] \vartheta(t-2 \pi) \)2 answers -
Demostrar si es lebesgue medible ​​​​​​​
5. Determine si la función de Dirichlet \[ f(x)=\left\{\begin{array}{l} 1, \text { si } x \in \mathbb{Q} \\ 0, \text { si } x \notin \mathbb{Q} \end{array}\right. \] es medible.0 answers -
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Calculate a and b for xi - xiii
3. For the following vector fields, compute the following: (a) \( \nabla \times \vec{F} \), (b) \( \nabla \cdot \vec{F} \), (c) \( \nabla \cdot(\nabla \times \vec{F}) \), (d) \( \nabla \times(\nabla \2 answers -
Do 2f
Determine whether the vector field \( \vec{F} \) is conservative for all \( \mathbb{R}^{2} \) or \( \mathbb{R}^{3} \), unless otherwise indicated. If so, find a function \( f \) such that \( \vec{F}=\2 answers -
A first-order system equivalent to the second order differential equation \( x^{\prime \prime}+2 x^{\prime}+x=2 \) is: \[ \begin{array}{l} x^{\prime}=y \\ y^{\prime}=x-2 x^{\prime}+2 \\ x^{\prime}=y \2 answers -
1) Solve the following ODE using the power series method (25 pts each) i) \( \quad y^{\prime \prime}+\sin (x) y^{\prime}+\cos (x) y=0 \) ii) \( \quad y^{\prime \prime}+\left(1-x^{2}\right) y=0 \)2 answers -
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[y = 2x^2 - 2x - 24] Escribe la cuadrática en forma de intersección y da los ceros de la función.1 answer
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explain the underlined steps in detail, please
\( \begin{aligned} \mathscr{L}\{y\} & =\frac{4+s}{s^{2}+4 s+13}+\frac{e^{-\pi s}+e^{-3 \pi s}}{s^{2}+4 s+13} \\ & =\frac{2}{3} \frac{3}{(s+2)^{2}+3^{2}}+\frac{s+2}{(s+2)^{2}+3^{2}}+\frac{1}{3} \frac{32 answers -
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