Advanced Math Archive: Questions from March 05, 2023
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1. Solve the following differential equations (D.E) (a) \( y^{\prime \prime}+y^{\prime}-2 y=0, \quad y(0)=1, \quad y^{\prime}(0)=4 \) (b) \( y^{\prime \prime}-2 y^{\prime}=30 e^{-3 t} \quad y(0)=1, \q2 answers -
4) - \( y^{\prime \prime}+y=\cos x-\sin x \) - \( \left(D^{2}+6 D+9 I\right) y=16 e^{-3 x} /\left(x^{2}+1\right) \) - \( \left(D^{2}+4 I\right) y=\cosh 2 x \)2 answers -
5. (8) \( y=\frac{x}{x^{2}+4},[0,3] \) Potential absolute max. \& min.: Absolute Min.: Location: Absolute Max.: Location:2 answers -
6AWW6: Problem 17 oint) Evaluate \( \iiint_{\mathcal{B}} f(x, y, z) d V \) for the specified function \( f \) and \( \mathcal{B} \) : \[ f(x, y, z)=\frac{z}{x} \quad 2 \leq x \leq 4,0 \leq y \leq 3,02 answers -
Una taza de café se enfría de \( 80^{\circ} \mathrm{C} \) a \( 60^{\circ} \mathrm{C} \) en cinco minutos a una temperatura ambiente de \( 10^{\circ} \mathrm{C} \). - Plantée la ecuación diferencia2 answers -
10, 13, and 16 please. solve using Laplace transform
10. \( y^{\prime \prime}-2 y^{\prime}+2 y=0 ; \quad y(0)=0, \quad y^{\prime}(0)=1 \) 11. \( y^{\prime \prime}-2 y^{\prime}+4 y=0 ; \quad y(0)=2, \quad y^{\prime}(0)=0 \) 12. \( y^{\prime \prime}+2 y^{2 answers -
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13 and 16 please. Use Laplace transform to solve the problem
10. \( y^{\prime \prime}-2 y^{\prime}+2 y=0 ; \quad y(0)=0, \quad y^{\prime}(0)=1 \) 11. \( y^{\prime \prime}-2 y^{\prime}+4 y=0 ; \quad y(0)=2, \quad y^{\prime}(0)=0 \) 12. \( y^{\prime \prime}+2 y^{2 answers -
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P5.3 (25 pts) Find a particular solution \( y_{p} \) of the given equation. (a) \( y^{\prime \prime}-y^{\prime}-2 y=3 x+4 \) (b) \( y^{\prime \prime}+16 y=e^{3 x} \) (c) \( y^{\prime \prime}+y=\sin x+2 answers -
Given \( f(x, y, z)=\sqrt{5 x^{2}+6 y^{2}+z^{2}} \) \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
Prove that y=xsen(x)+xcos(x) is a solution to the diferential equation y''+y=2cos(x)-2
Compruebe que \( \mathrm{y}=\mathrm{x} \operatorname{sen}(\mathrm{x})+\mathrm{x} \cos (\mathrm{x}) \) es una solución de la ecuación diferencial \[ y^{\prime \prime}+y=2 \cos (x)-2 \]2 answers -
Determine if each equation is: a. separable b. linear c. cant determine it d. neither of the previous choices show all calculations
DETERMINE: MUESTRE TODO SU TRABAJO 1. La ecuación \( \frac{d y}{d x}=10-\mathrm{y} \) es: a. Separable b. Lineal c. No la puedo determinar d. Ninguna de las anteriores 2. \( \frac{d y}{d x}=\frac{x-y2 answers -
Using the following properties of a twice-differentiable function \( y=f(x) \), select a possible graph of \( f \). A. \( B \). c. D.2 answers -
Given \( f(x, y, z)=\sqrt{4 x^{2}+2 y^{2}+1 z^{2}} \), find \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
Given \( f(x, y, z)=\sqrt{5 x+2 y-6 z} \), \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
Given \( f(x, y)=7 x^{8} \cos \left(y^{4}\right) \), find \[ \begin{array}{c} f_{x y}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
Given \( f(x, y)=-3 x^{6}+4 x^{2} y^{2}-2 y^{3} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]2 answers -
The solution of the differential equation \( x y \frac{d y}{d x}=2+x+2 y+x y \) Select one: \[ \begin{array}{l} y=x+\ln \left[x^{2}(1-y)\right]+c \\ y=x-\ln \left[x^{2}(1-y)\right]+c \\ y=x+\ln \left[2 answers -
The solution of the differential equation \( x y \frac{d y}{d x}=2+x+2 y+x y \) Select one: \[ \begin{array}{l} y=x+\ln \left[x^{2}(1-y)\right]+c \\ y=x-\ln \left[x^{2}(1-y)\right]+c \\ y=x+\ln \left[2 answers -
(1 point) Determine \( x \) and \( y \) such that \[ \left[\begin{array}{ccc} 4 & -1 & 2 \\ 3 & -4 & 2 \end{array}\right]+\left[\begin{array}{ccc} x-y & 3 & 4 \\ 2 & x & -4 \end{array}\right]=\left[\b2 answers -
(25 pts) Find a particular solution \( y_{p} \) of the given equation. (a) \( y^{\prime \prime}-y^{\prime}-2 y=3 x+4 \) (b) \( y^{\prime \prime}+16 y=e^{3 x} \) (c) \( y^{\prime \prime}+y=\sin x+\cos2 answers -
\( \begin{array}{c}p=3 x+2 y \text { subject to } \\ 1.8 x+0.9 y \leq 9 \\ 0.03 x+0.06 y \leq 0.3 \\ 9 x+9 y \leq 54 \\ x \geq 0, y \geq 0\end{array} \)2 answers -
Identify the differential equation that produces the following differential equation. \[ \begin{array}{l} y^{\prime}=y(2-y) \\ y^{\prime}=y(y-2) \\ y^{\prime}=y^{2}(y-2)^{2} \\ y^{\prime}=y(y-2)^{2} \2 answers -
Given: \[ \begin{aligned} f(x) & =\left\lceil\frac{x}{5}\right\rceil \quad g(x)=2^{x} \\ (f \circ g)(3) & = \end{aligned} \]2 answers -
(1 point) Let \( \vec{x}=\left[\begin{array}{c}2 \\ 6 \\ -2\end{array}\right] \) and \( y=\left[\begin{array}{c}-6 \\ 0 \\ 3\end{array}\right] \). Find the vectors \( \vec{v}=6 \vec{x}, \vec{u}=\vec{x2 answers -
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