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Advanced Math Archive: Questions from February 06, 2023

• ​​​​​​​​​​​​​​​​​​​​​ punto 1 e incisos
  1. Para la siguiente función obtén la derivada por cada uno de los métodos mencionados y calcula el error relativo para cada formula. \[ f(x)=\left(\frac{3 x-1}{x^{2}+3}\right)^{2} \] a) Método an
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  15. Solve the initial value problem \( (\cos (y)+y \cos (x)) d x+(\sin (x)-x \sin (y)) d y=0, \quad y(0)=-1 \)
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• ​​​​​​​NEED Solution for 4 and 5 please
  4. \( y^{\prime \prime}+2 y^{\prime}+2 y=10 \sin 4 x \). 5. \( y^{\prime \prime}+2 y^{\prime}+4 y=13 \cos 4 x \). 6. \( y^{\prime \prime}-3 y^{\prime}-4 y=16 x-12 e^{2 x} \). 7. \( y^{\prime \prime}+6
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• f(x)=4x^(3)-28x^(2)+47x-35 mas. Enter exact value, not decir
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• hallar la transformada de la place utilizando heavyside:
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• Just (d). T3(X) means the 3rd Taylor polynomial of f.
  Find \( T_{3}(\mathbf{X}) \) (a) \( f(x, y)=e^{x} \cos y, \quad \mathbf{X}_{0}=(0,0) \) (b) \( f(x, y)=e^{-x-y}, \quad \mathbf{X}_{0}=(0,0) \) (c) \( f(x, y, z)=(x+y+z-3)^{5}, \quad \mathbf{X}_{0}=(1,
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  Let \( K=\left[\begin{array}{ccc}2 & y & -4 \\ -1 & 2 & 4 \\ x & 4 & 0\end{array}\right] \) be a symmetric matrix. Find the values of \( x \) and \( y \) : \[ \begin{array}{l} x=4, y=1 \\ x=-4, y=-1 \
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• 1) Eigenvector associated to the eigenvalue λ = −4 2) Eigenvector associated to the eigenvalue λ = −3 3) Eigenvector associated with the eigenvalue λ = 0 4) Eigenvector associated with the eige
  1. Para la matriz respecto a las siguientes categorias: \[ \mathrm{A}=\left[\begin{array}{rrrr} 65 & -36 & 10 & -8 \\ -117 & 75 & -27 & 9 \\ -359 & 234 & -76 & 38 \\ 614 & -366 & 118 & -62 \end{array}
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  Find the partial derivatives \( f_{x} \) and \( f_{y} \) if \( f(x, y)=15 x^{2} y^{3}+7 x y^{2}-4 x^{2} \). \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]
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  3. Solve the following DEs/IVPs. (a) \( \left(e^{x}-3 x^{2} y^{2}\right) y^{\prime}=2 x y^{3}-y e^{x} \) (b) \( \frac{d y}{d x}+y=y^{2}(x-1), y(0)=1 \) (c) \( -1+\left(y^{\prime}\right)^{2}+y y^{\prim
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  What is the particular solution for the following differential equation. \[ \begin{array}{c} y^{\prime \prime}-25 y=0, y(0)=10, y^{\prime}(0)=10 \\ y=6 e^{5 t}+4 e^{-5 t} \\ y=10 e^{5 t}+t e^{5 t} \\
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