Advanced Math Archive: Questions from October 10, 2022
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(1 point) Solve the initial value problem. \[ (-6 \tan y-2) d x+\left(-6 x \sec ^{2} y+1 / y\right) d y=0 \] with \( y(0)=1 \).2 answers -
Domino Cards: 1 B-2 Mnminn Carde: 2 Above is a set of dominoes. If you want, you can print them out and cut out each pair. Like dominoes that have dots on both sides, most of the time the number of2 answers -
2) Determine \( f(x) \), if a) \( f(x)=o\left(\frac{1}{x}\right), x \rightarrow \infty \) b) \( f(x)=O\left(\frac{1}{x}\right), x \rightarrow 0 \)2 answers -
1 answer
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Find an explicit general solution for 1) \( y^{\prime}=\frac{8}{x} \Rightarrow y= \) \( +C \) 2) \( y^{\prime}=-3 \sin x+3 \cos x \Rightarrow y= \) 3) \( y^{\prime}=6 e^{x} \Rightarrow y= \) \( +C \)2 answers -
Función objetivo: \[ \begin{aligned} Z \min =250000 &\left(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}+x_{6}\right)+350000\left(55+0.85\left(55+x_{1}\right.\right.\\ &+0.85\left(0.85\left(55+x_{1}\right)+x_{2}\rig2 answers -
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Determine if the IVP of the DE has a solution and if the solution (if exists) is unique
Determina si el P.V.I. \( \frac{d y}{d x}=x^{2}-x y^{3} ; y(1)=6 \) tiene solución y si la solución (de exisitir) es única.0 answers -
Determine under what conditions the ordinary differential equation will have a unique solution.
1) Determina bajo que condiciones la EDO \( \frac{d y}{d x}=\frac{2 y}{x} \) tendrá solución única.2 answers -
Determine under what conditions the ordinary differential equation will have a unique solution.
2) Determina bajo que condiciones el PVI \( \frac{d y}{d x}=\frac{2 y}{x} ; y(0)=6 \) tendrá solución única.2 answers -
Solve the ED with homogeneous coefficients: this is what I have so far but not sure if its okay
4. (11 puntos) Resuelva la ecuación diferencial con coeficientes homogéneos \( \left(x^{2}+2 y^{2}\right) d x-x y d y=0, \quad y(-1)=1 . \). \( \left(x^{2}+2 y^{2}\right) d x-x y d y=0 \) * Homogé2 answers -
13 and 14 please
13. \( y^{\prime \prime}-2 y^{\prime}+y=t e^{t}+4, \quad y(0)=1, \quad y^{\prime}(0)=1 \) 14. \( y^{\prime \prime}+4 y=3 \sin (2 t), \quad y(0)=2, \quad y^{\prime}(0)=-1 \)2 answers -
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SOLVE BY THE METHOD OF SEPARATION OF VARIABLES:
\( y^{\prime}=\frac{x}{y} \) \( y^{\prime}=2^{x-y} \) \( y^{\prime}=\cos 2 x-4+x \)2 answers -
Solve the initial value problem \( y^{\prime \prime}+y^{\prime}-6 y=12 e^{-2 x} \) with \( y(0)=0, y^{\prime}(0)=7 \).2 answers -
5. Sea \( p^{*} \) el vector solución de (1) tal que \( g^{T} p^{*} \neq 0 \). Demuestre que \( \nabla f(\hat{x})^{T} p^{*}0 answers -
7. Halle las ecuaciones paramétricas para la regla que pasa por los puntos \( (4,-1,2) \) y \( (1,1,5) \) 8. Grafique los puntos y la recta del ejercicio anterior 7. Find the parametric equations for0 answers -
9. Dibuje un plano que pase por el punto \( (1,0,-1) \) 10. Halle la ecuacion de un plano que pase por el punto ( \( 1,2,-2) \) y que contiene a oa recta \( x=2 t, y=3-t, z=1+3 t \) 9. Draw a plane th0 answers -
\( \begin{aligned}-47 x_{1}+4 x_{2}-7 x_{3} &=-118 \\ 19 x_{1}-3 x_{2}+2 x_{3} &=43 \\-15 x_{1}+5 x_{2} &=-25 \end{aligned} \)0 answers -
Solve the EDLNH of order 3 and constant coefficients. Use the method of undetermined coefficients
Problema: Resuelve la EDLNH de orden 3 y coeficientes constantes. Use el método de coeficientes indeterminados \[ y^{\prime \prime \prime}-2 y^{\prime \prime}+y^{\prime}=2-24 e^{x}+40 e^{5 x}, y(0)=\2 answers -
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3. Determine \( \mathcal{L}\{y(t)\} \) (a) (b) \[ y^{\prime \prime}+2 y^{\prime}-2 y=2, \quad y(0)=1, \quad y^{\prime}(0)=1 \] \[ 9 y^{\prime \prime}+12 y^{\prime}+4 y=0, \quad y(0)=2, \quad y^{\prime2 answers -
Translation: Integrate the following step by step.
10 Integre lo siguiente paso a paso \( f(x)=15 \int_{0}^{10} e^{-15(x-20)} d x \)2 answers