Advanced Math Archive: Questions from November 10, 2022
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2 answers
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\( y^{\prime \prime}+4 y^{\prime}+5 y=3 x+4 e^{-3 x} \) \( y^{\prime \prime}+4 y^{\prime}+5 y=3 x+4 e^{-3 x} \)2 answers -
If \( y=\frac{\sin x}{1-x^{2}} \), show that \[ \left(1-x^{2}\right) y^{\prime \prime}-4 x y^{\prime}-\left(1+x^{2}\right) y=0 \]2 answers -
2 answers
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2 answers
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Sea \( A \) una matriz de dimensión \( 6 \times 8 \). El rango de \( A \) es 3 . ¿Cuántos parámetros son necesarios para describir el conjunto de soluciones del sistema \( A \vec{x}=\overrightarro2 answers -
(i) Find the centres of the following \( \mathbb{k} \)-algebras. - \( A_{1}=\left\{\left(\begin{array}{ccc}x & 0 & 0 \\ y & x & 0 \\ z & 0 & x\end{array}\right) \mid x, y, z \in \mathbb{k}\right\} \)2 answers -
Solve the following system: \[ \begin{array}{r} x^{\prime}=3 x-y-z \\ y^{\prime}=x+y-z \\ z^{\prime}=x-y+z \end{array} \]2 answers -
Fill in the blank so that the resulting statement is true. \[ \tan (\alpha-\beta)= \] Choose the correct answer. A. \( \tan (\alpha-\beta)=\frac{\tan \alpha+\tan \beta}{1+\tan \alpha \tan \beta} \) B.2 answers -
(2 points) Solve the initial value problem \[ y^{\prime \prime}+3 x y^{\prime}-12 y=0, y(0)=9, y^{\prime}(0)=0 \text {. } \] \[ y= \]2 answers -
2 answers
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0 answers
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\( y^{\prime} \) if \( y=\left(x^{9}+1\right)^{12 x+15} \) \( y^{\prime}=\left(x^{9}+1\right)^{12 x+15}\left[\frac{12(9) x^{8}}{x^{9}+1}\right] \) \( y^{\prime}=\left(x^{9}+1\right)^{12 x+15}\left[122 answers -
\( y^{\prime} \) (or \( \frac{d y}{d x} \) if \( \ln (5 y) \cos x=y^{4}+19 x y \) \( y^{\prime}=\frac{19 y+\ln (5 y) \sin (x)}{\cos (x)-19 x y-4 y^{4}} \) \( y^{\prime}=\frac{19 y^{2}+y \ln (5 y) \sin2 answers -
please help (verify identity)
verify identity \[ \begin{array}{l} \text { a } \sin 2 x=\frac{2(\tan x-\cot x)}{\tan ^{2} x-\cot ^{2} x} \\ \text { b } \frac{1+\tan ^{2} u}{1-\tan ^{2} u}=\frac{1}{\cos ^{2} u-\sin ^{2} u} \\ \text1 answer -
The negation of \( \forall x \exists y \forall z[B(x, y) \wedge((z \neq y) \rightarrow \neg B(x, z))] \) is a) \( \exists x \forall y \exists z[\mathrm{~B}(\mathrm{x}, \mathrm{y}) \wedge((\mathrm{z}=\2 answers -
Solve using Variation of Parameters. If possible, show the process.
\( y^{\prime \prime}+8^{2} y=2 \sin ^{2}(8 x), \quad y(0)=5, \quad y^{\prime}(0)=7 \)2 answers -
Solve the following ODE: \( y^{\prime \prime}+4 y^{\prime}+5 y=\delta(t-1), y(0)=0, y^{\prime}(0)=3 \)2 answers -
4. Encontrar \( \int_{C} R e(z) d z \) Si \( C: y=x^{2} \) desde \( -1+i \) hasta \( 2+4 i \) a) Mediante integración directa b) Parametrizando la recta2 answers -
Solve the following contour problem, [eq] for the following cases: a) [eq] b) [eq] kindly do both parts
Resuelva el siguiente problema de contorno, \[ \left\{\begin{array}{l} u_{t t}=a^{2} \frac{1}{r} \frac{\partial}{\partial r} r \frac{\partial u}{\partial r}+A r^{2}, \quad 00 answers -
Solve the given initial-value problem. \[ y^{\prime \prime}+x\left(y^{\prime}\right)^{2}=0, y(1)=3, y^{\prime}(1)=2 \] \[ y= \]2 answers -
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Find the indicated partial derivative. \[ f(x, y, z)=e^{x y z^{5}} ; \quad f_{x y z} \] \[ f_{x y z}(x, y, z)= \]2 answers -
( 1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-16 y^{\prime \prime}+63 y^{\prime}=48 e^{x} \] \[ \begin{array}{l} y(0)=17, \quad y^{\prime}(0)=18, \quad y^{\prime \pri2 answers -
2 answers
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Solve the initial value problem \[ \begin{array}{c} y^{\prime \prime}-y^{\prime}+2 y=3 e^{-x}-10 \cos 3 x \\ y(0)=1, y^{\prime}(0)=2 \end{array} \]2 answers -
simplex method
Maximize \( F=5 x+12 y \) s.t. \[ \begin{array}{l} 3 x+y \leq 12 \\ x+2 y \leq 12 \\ x, y \geq 0 \end{array} \]2 answers -
\( (\cos x) \frac{d y}{d x}+y \sin x=4 x \cos ^{2} x, \quad y\left(\frac{\pi}{4}\right)=\frac{9 \pi^{2} \sqrt{2}}{16} \)2 answers -
Analizar y dibujar la gráfica de \( f(x)=x^{4}-12 x^{3}+48 x^{2}-64 x \) respondiendo los siguiente: a) Primera derivada b) Segunda derivada c) Intersecciones con el eje \( x \) d) Intersección con1 answer -
solve 21,24
In Problems \( 21-30 \) use the Laplace transform to solve the given initial-value problem. 21. \( y^{\prime}+4 y=e^{-4 t}, \quad y(0)=2 \) 22. \( y^{\prime}-y=1+r e^{t}, y(0)=0 \) 23. \( y^{\prime \p2 answers -
Find the Jacobian. \( \frac{\partial(x, y, z)}{\partial(s, t, u)} \), where \( x=4 s-3 t-2 u, y=3 s-2 t-4 u, z=4 s-2 t+2 u \) \[ \frac{\partial(x, y, z)}{\partial(s, t, u)}= \]2 answers