Other Math Archive: Questions from March 13, 2023
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(1 point) Solve \[ \begin{array}{l} x-y+z-w=4 \\ y+2 z+w=3 \\ -z+w=2 \\ -x+2 y-3 z+5 w=1 \\ x= \\ y= \\ z=, w= \\ \end{array} \]2 answers -
The domain of \( f(x, y)=\ln \left(\sqrt{x^{2}+y^{2}}\right) \) is a. \( \left\{(x, y) \in \mathbb{R}^{2} \mid x \geq 0, y \geq 0\right\} \) b. \( \mathbb{R}^{2}-\{(0,0)\} \) c. \( \left\{(x, y) \in \2 answers -
Find the general solution to the following DEs: (a) \( y^{\prime \prime}-2 y^{\prime}+2 y=e^{2 x}(\cos x-3 \sin x) \). (b) \( y^{\prime \prime \prime}-y^{\prime \prime}-4 y^{\prime}+4 y=5-e^{x}+e^{2 x2 answers -
(1 point) Solve: \[ \begin{array}{l} \left(\begin{array}{cc} 2 x & y+4 \\ z-4 & w \end{array}\right)=\left(\begin{array}{ll} 7 & 6 \\ 8 & 3 \end{array}\right) \\ x= \\ y= \\ z= \\ w= \\ \end{array} \]2 answers -
- Solve the equation as a separable case to find tge implicit solution. - Express the answer as an explicit solution.
Problema 6. Use la ecuacion \[ \frac{d y}{d x}=\frac{x y-2 x+3 y-6}{2 x+4} \] (ISpts) Resuetva la ecuación como un caso separable para encontrar la solución implicita. (Spts) Exprese la respuesta co2 answers -
- Verify that y=c1e^x+c2e^4x satisfy the equation y"- 5y' + 4y = 0 - Find the values of c1 y c2 (the parameters) for the problem y"- 5y'+ 4y = 0 with y = c1e^x + c2e^4x and the values for y(1) = 2, y'
Problema 3. Use las ecuaciones: \( y=c_{1} e^{x}+c_{2} e^{4 x}, y^{\prime \prime}-5 y^{\prime}+4 y=0 \) (5pts) Verifique que \( y=c_{1} e^{x}+c_{2} e^{4 x} \) satisface la ecuación \( y^{\prime \prim2 answers -
Tema: matrices y ecuaciones lineales
ncontrar la solución al siguiente sistema de ecuaciones lineales: (usar el Método que el estudiante decida) \[ \begin{array}{c} x+y+z=3 \\ -2 x-y+z=1 \\ 3 x+y-2 z=-2 \end{array} \]2 answers -
Solve the following initial value problem. \[ y^{\prime \prime \prime}-4 y^{\prime \prime}+y^{\prime}+6 y=0 ; \quad y(0)=-1, \quad y^{\prime}(0)=3, \quad y^{\prime \prime}(0)=-3 \]2 answers -
2 answers
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4.2. Los planes secretos de Marlana Fine ac the das to oonplese the puank 1. 1. Mariana estudia aysl. 2. Marianu congra ropu aqui: 3. Mariana deponia an cheque aqua. 4. A Mariana le guta ver arte aqui0 answers -
2 answers
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Solve using Laplace's method of solution \[ y^{\prime \prime}+9 y=e^{t}, \quad y(0)=0, y^{\prime}(0)=0 \] \[ y^{\prime \prime}-6 y^{\prime}+9 y=t^{2} e^{3 t}, \quad y(0)=2, y^{\prime}(0)=6 \] \[ y^{\p2 answers -
solve tge vip
\( \begin{array}{l}\text { 0. }\left(D^{3}+3 D^{2}+3 D+I\right) y=8 \sin x, \quad y(0)=-1 \\ y^{\prime}(0)=-3, y^{\prime \prime}(0)=5\end{array} \)2 answers -
(a) Determine whether \( (x-y) \mid\left(x^{n}-y^{n}\right), \forall n \in \mathbf{Z}^{+} \)and \( x, y \in \mathbf{Z}, x \neq y \). (b) Determine whether \( 6 \mid\left(n^{3}-n\right) \), for each in2 answers