Advanced Math Archive: Questions from September 29, 2022
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2 answers
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10.Solve the boundary-value problem \( (B V P) \) \[ y^{\prime \prime}+2 y^{\prime}+2 y=0, y(0)=1, y^{\prime}\left(\frac{\pi}{2}\right)=0 \]2 answers -
Determine si los siguientes vectores forman una base en \( \mathrm{R}^{3} \). 1. \( \{(1,5,3),(2,3,4),(1,9,1)\} \) 2. \( \{(0,2,6),(1,2,3),(3,4,8)\} \) Demuestre el procedimiento completo como se mues1 answer -
Conteste el siguiente problema : Halle la primera derivada de la siguiente función utilizando la definición de limite. No las formulas. \( f(x)=3 x^{2}+2 x+10 \) \[ \lim _{h \rightarrow 0} \frac{f(x2 answers -
Solve the exact equation, \( \left(e^{x}+y\right) d x+(x-\sin y) d y=0 \) a. \( e^{2 x}+y x+\cos y=C \) b. \( e^{x}+y x^{2}+\cos y=C \) c. \( e^{x} x+y x+\sin y=C \) d. \( e^{x}+y x+\cos y=C \)2 answers -
\[ \frac{d y}{d x}=e^{2 x}(\sec y) \] a. \( \cos y=\frac{1}{2} e^{3 x}+C \) b. \( \quad \sin y=\frac{1}{2} e^{3 x}+C \) c. \( \sin y=\frac{1}{2} e^{2 x}+C \) d. \( \quad \cos y=\frac{1}{2} e^{2 x}+C \2 answers -
2 answers
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2 answers
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Solve the separable initial value problem. 1. \( y^{\prime}=6 e^{3 x}\left(1+y^{2}\right), y(0)=1 \Rightarrow y= \) 2. \( y^{\prime}=9 x^{2} \sqrt{1+x^{3}}\left(1+y^{2}\right), y(0)=0 \Rightarrow y= \2 answers -
3. Solve each of the following de’s- you need the general solution. (i) y’’’’ - y = 0; (ii) y’’’’ - y = x^2; (iii) y’’’’ - y = sin (2x); (iv) y’’’’ - y = e^x.
Solve each of the following de's- you need the general solution. (i) \( y^{\prime \prime \prime}-y=0 \); (ii) \( y^{\prime \prime \prime}-y=x^{\wedge} 2 \); (iii) \( y^{\prime \prime \prime}-y=\sin (22 answers -
.et \( f(x, y, z)=\frac{x^{2}-3 y^{2}}{y^{2}+5 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]2 answers -
Calculate all four second-order partial derivatives of \( f(x, y)=(5 x+4 y) e^{y} \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
Task \( 1(1+1+2+2 \mathrm{pt}) \). Solve the following nonhomogeneous ODEs. (a) \( y^{\prime \prime}-4 y^{\prime}+3 y=e^{x} \); (b) \( y^{\prime \prime}=y+e^{x} \cos (2 x) \); (c) \( y^{\prime \prime}2 answers -
#12 and #18 Please
In Problems \( 1-26 \), solve the given differential equation by undetermined coefficients. 1. \( y^{\prime \prime}+3 y^{\prime}+2 y=6 \) 2. \( 4 y^{\prime \prime}+9 y=15 \) 3. \( y^{\prime \prime}-102 answers -
Given \( f(x, y)=-\left(9 x^{4} y+9 x y^{6}\right) \). Compute: \[ \frac{\partial^{2} f}{\partial x^{2}}= \] \[ \frac{\partial^{2} f}{\partial y^{2}}= \]2 answers -
SOLVE WITH DETAIL PLEASE. ONLY D, please.
4. Solve the initial value problem. (a) \( y^{\prime}=-x e^{x}, \quad y(0)=1 \) (b) \( y^{\prime}=x \sin x^{2}, \quad y\left(\sqrt{\frac{\pi}{2}}\right)=1 \) (c) \( y^{\prime}=\tan x, \quad y(\pi / 4)2 answers -
SOLVE WITH DETAIL PLEASE. Only C.
Find all of the equation. (a) \( y^{\prime}=-x \) (c) \( y^{\prime}=x \ln x \) (e) \( y^{\prime \prime}=2 x e^{x} \) (g) \( y^{\prime \prime \prime}=-\cos x \) (i) \( y^{\prime \prime \prime}=7 e^{4 x2 answers -
#18
In Problems \( 1-26 \), solve the given differential equation by undetermined coefficients. 1. \( y^{\prime \prime}+3 y^{\prime}+2 y=6 \) 2. \( 4 y^{\prime \prime}+9 y=15 \) 3. \( y^{\prime \prime}-102 answers -
resolve
esuelva \( 3 y^{\prime \prime}-6 y^{\prime}+6 y=e^{x} \sec x \) \( y=c_{1} e^{x} \cos x+c_{2} e^{x} \sin x+\frac{1}{3} e^{x} \cos x \ln (\cos x)+\frac{1}{3} x e^{x} \sin x \) \[ y=c_{1} e^{x} \cos x+c2 answers -
resolve
esuelva \( 3 y^{\prime \prime}-6 y^{\prime}+6 y=e^{x} \sec x \) \( y=c_{1} e^{x} \cos x+c_{2} e^{x} \sin x+\frac{1}{3} e^{x} \cos x \ln (\cos x)+\frac{1}{3} x e^{x} \sin x \) \[ y=c_{1} e^{x} \cos x+c2 answers -
Solve the separable initial value problem. 1. \( y^{\prime}=2 x \cos \left(x^{2}\right)\left(1+y^{2}\right), y(0)=5 \Rightarrow y= \) 2. \( y^{\prime}=\ln (x)\left(1+y^{2}\right), y(1)=5 \Rightarrow y2 answers -
Perform the following integrations: 1) \( y^{\prime}=5 e^{5 x} \sin \left(e^{5 x}\right) \Rightarrow y= \) \( +C \) 2) \( y^{\prime}=\frac{x+3}{x^{2}+6 x+13} \Rightarrow y= \) \( +C \) 3) \( y^{\prime2 answers -
Problem 6,12,18
EXERCISES \( 4.4 \) Answers to selected odd-numbered problems begin In Problems \( 1-26 \) solve the given differential equation by undeter- 9. \( y^{\prime \prime}-y^{\prime}=-3 \) mined coefficients2 answers -
Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-4 y^{\prime \prime}-y^{\prime}+4 y=0 \] \[ \begin{array}{l} y(0)=-3, \quad y^{\prime}(0)=-6, \quad y^{\prime \prime}(0)=-33 \\ y(x)2 answers -
ONLY NEED HELP ON NUMBER 3
Perform the following integrations: 1) \( y^{\prime}=5 e^{5 x} \sin \left(e^{5 x}\right) \Rightarrow y= \) \( +C \) 2) \( y^{\prime}=\frac{x+3}{x^{2}+6 x+13} \Rightarrow y= \) \( +C \) 3) \( y^{\prime2 answers -
please need help
Suelva \( y^{\prime \prime}+y=\cos ^{2} x \) \[ y=c_{1} \cos x+c_{2} \sin x+\frac{1}{3} \cos ^{4} x-\frac{1}{3} \sin ^{2} x \] \[ y=c_{1} \cos x+c_{2} \sin x+\frac{1}{3}+\frac{1}{3} \sin ^{2} x \] \[2 answers -
Solucione numéricamente el problema planteado anteriormente, mediante el uso del algoritmo de Euler para una ecuación diferencial ordinaria de segundo orden.
\( x^{\prime \prime}+x=0, \quad \operatorname{con} x(0)=-1 \) y \( x^{\prime}(0)=8 \) \( \mathcal{L}\left\{x^{\prime \prime}+x\right\}=\mathcal{L}\{0\} \quad \rightarrow \quad \mathcal{L}\left\{x^{\pr2 answers -
Graph the inequalities and find the intersection (corner) points: 1. \[ \begin{array}{l} x+y \leq 12 \\ 2 x+y \leq 16 \\ x \geq 0, y \geq 0 \end{array} \] 2. \[ \begin{array}{l} x+y \leq 7 \\ x+2 y \l2 answers -
2 answers
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(6 pts) Solve the following ODEs. a) (1 pt) \( y^{\prime \prime}-7 y^{\prime}+10 y=e^{t} \); b) \( (1 \mathrm{pt}) y^{\prime \prime}=y+e^{2 t} \cos t \) c) (2 pts) \( y^{\prime \prime}-2 y^{\prime}+y=2 answers -
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23. Maximize \[ Z=14 x-3 y \] subject to \[ \begin{array}{l} y \geq 12.5-4 x \\ y \leq 9.3-x \\ y \geq 4.7+0.8 x \end{array} \]2 answers