Advanced Math Archive: Questions from November 01, 2022
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2. Find the general solution of the following ODEs (a) \( y^{\prime \prime}-4 y=0 \) (b) \( y^{\prime \prime}+4 y=0 \) (c) \( y^{\prime \prime}+4 y^{\prime}=0 \) (d) \( y^{\prime \prime}+4=0 \)2 answers -
0 answers
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(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}+49 y^{\prime}=0 \] \[ \begin{array}{l} y(0)=6 \quad v^{\prime}(\cap)=56 \quad v^{\prime \prime}(\cap)=-98 \\ y(x) \end{ar2 answers -
ize \( p=10 x+10 y+15 z s \) \( x-y+z \leq 12 \) \( 2 x-2 y+z \geq 13 \) \( -y+z \geq 1 \) \( x \geq 0, y \geq 0, z \geq 0 \)2 answers -
Solve the following IVPs
3. Solve the following IVPs: (3.1) \( 6 y^{\prime \prime}+y^{\prime}-y=0, \quad y(0)=-1, \quad y^{\prime}(0)=2 \) (3.3) \( \quad y^{\prime \prime}-2 y^{\prime}+5 y=0, \quad y(-1)=0, \quad y^{\prime}(-2 answers -
Given the function \( f(x, y)=3 x^{2}+x y^{2} \), find the Hessian, \( \nabla_{(x, y)}^{2} f(x, y) \)2 answers -
2 answers
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\( c=4 x+y+4 z \) subjec \( x+y+z \geq 100 \) \( 2 x+y \geq 50 \) \( y+z \geq 50 \) \( x \geq 0, y \geq 0, z \geq 0 \)2 answers -
\( p=3 x+5 y+6 z \) subj \( x+y+z \leq 150 \) \( x+y+z \geq 100 \) \( x \geq 0, y \geq 0, z \geq 0 \)2 answers -
Bxercise \( 20.9 \) Show that \[ \vec{\nabla} \times(\vec{\nabla} \times \vec{A}(x, y, z))=\vec{\nabla}(\vec{\nabla} \cdot \vec{A}(x, y, z))-\nabla^{2} \vec{A}(x, y, z) \]2 answers -
\( y^{\prime \prime}-4 y^{\prime}+4 y=\frac{e^{2}}{1+x} \). \( y^{\prime \prime}-2 y^{\prime}+y=e^{x} \ln x \).2 answers -
3. \( f(x, y, z)=\frac{x-y}{y^{2}+z^{2}} \) a. \( f(3,-1,2) \) b. \( f\left(1, \frac{1}{2},-\frac{1}{4}\right) \) c. \( f\left(0,-\frac{1}{3}, 0\right) \) d. \( f(2,2,100) \)2 answers -
1) Solve the following ODE using the power series method i) \( y^{\prime \prime}+\sin (x) y^{\prime}+\cos (x) y=0 \) ii) \( y^{\prime \prime}+\left(1-x^{2}\right) y=0 \) 2) For the following ODE deter2 answers -
5,7,11 please
In Exercises 5-12, find and sketch the domain for each function. 5. \( f(x, y)=\sqrt{y-x-2} \) 6. \( f(x, y)=\ln \left(x^{2}+y^{2}-4\right) \) 7. \( f(x, y)=\frac{(x-1)(y+2)}{(y-x)\left(y-x^{3}\right)2 answers -
Let V⊂R3 be the vector space spanned by the vectors v⃗ 1=⎛⎝⎜1110⎞⎠⎟ and v⃗ 2=⎛⎝⎜1−112⎞⎠⎟ and let W⊂R3 be the vector space spanned by the vectors w⃗ 1=⎛⎝⎜12−
Sea \( V \subset \mathbb{R}^{3} \) el espacio vectorial generado por los vectores \[ \vec{v}_{1}=\left(\begin{array}{c} 1 \\ 1 \\ 10 \end{array}\right) \mathrm{y} \vec{v}_{2}=\left(\begin{array}{c} 12 answers -
Consider the arrays Then the set {A,B,C} is linearly dependent for f equal to:
Considere las matrices \[ A=\left(\begin{array}{cc} 1 & 3 \\ -7 & 0 \end{array}\right), B=\left(\begin{array}{cc} 1 & 4 \\ 0 & 0 \end{array}\right), C=\left(\begin{array}{cc} 1 & 10 \\ f & 0 \end{arra2 answers -
2) For the following ODE determine if the method of Frobenius can be used. i) \( \quad(x+2)^{2} y^{\prime \prime}+(x+2) y^{\prime}-y=0 \) ii) \( 2 x(x-1) y^{\prime \prime}-(x+1) y^{\prime}+y=0 \) iii)2 answers -
114. 4. the equat \( \mathrm{n} \) of the two tangent lines to the circle \( x^{2}+y^{2}=4 \) and parallel to the lin \[ \begin{array}{lr} y=-\sqrt{8}+10 \text { is } & \\ 1-y=\sqrt{-6} & 3-y=\sqrt{8}2 answers