Advanced Math Archive: Questions from April 11, 2023
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\( \begin{array}{l}\frac{d y}{d x}=x^{3}\left(y^{2}-x^{2}\right)+\frac{y}{x} \\ y^{2} \frac{d y}{d x}+\cos y=x\end{array} \)2 answers -
\( \begin{array}{l}\text { ii) } x=\frac{7 T^{-1}-2 T^{-3}}{T} \quad y=\frac{2 T^{3}}{T^{2}} \\ \text { Quotient } \\ \text { Rule } \\ y=\frac{\left(3 x^{-1}-4 x\right)^{6}}{(x-1)^{2}} \quad \frac{d2 answers -
5. \( \iiint_{E}\left(1 / x^{3}\right) d V \), where \( E=\left\{(x, y, z) \mid 0 \leqslant y \leqslant 1,0 \leqslant z \leqslant y^{2}, 0 \leqslant x \leqslant z+1\right\} \) \[ \begin{array}{l} \tex2 answers -
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BONUS. [4 points] Since y = sin x is a solution of the differential equation y(4)+2y+11y"+2y' + 10y=0 , find the general solution.
Dado que \( y=\sin x \) es solución de la ecuación diferencial \( y^{(4)}+2 y^{\prime \prime \prime}+11 y^{\prime \prime}+2 y^{\prime}+10 y=0 \) , halla la solución general.2 answers -
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parear cada numero con la letra que mejor defina el concepto
Pareo \#1 34 puntos - 1. Función de ingresos A Aumentan o disminuyen conforme aumenta o disminuye el nivel de producción - 2. Differential cost (Costo diferencial) B Se mantiene constante, aunque au2 answers -
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Solve the following system
\( \begin{array}{l}5 x^{\prime}+y^{\prime}-3 x+y=0 \\ 4 x^{\prime}+y^{\prime}-3 x=-t\end{array} \)2 answers -
Use the Laplace transform to solve the initial value problems: 1. \( y^{\prime \prime}+4 y^{\prime}+5 y=e^{-t}(\cos t+3 \sin t), y(0)=0, y^{\prime}(0)=4 \) 2. \( y^{\prime \prime}+2 y^{\prime}+2 y=2 t0 answers -
1002) \( A=4 \) and \( B=9 \) in \( F \) ig. 1002, determine: 1) \( y(2.0), 2) y(6.0) \), 3) \( y(14.0) \), 4) \( y^{\prime}(2.0) \), 5) \( \left.y^{\prime}(6.0), 6\right) y^{\prime}(10.0) \), 7) \( \2 answers -
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Sean A y B matrices sesgadas simétricas de nxn. Demostrar que AB es asimétrico si y solo si AB = -BA1 answer
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