Advanced Math Archive: Questions from May 11, 2023
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Solve the initial value problem: \[ \mathbf{y}^{\prime}=\left[\begin{array}{ccc} -1 & -4 & -1 \\ 3 & 6 & 1 \\ -3 & -2 & 3 \end{array}\right] \mathbf{y}, \quad \mathbf{y}(0)=\left[\begin{array}{c} -2 \2 answers -
C. Find the general solution a) \( y^{(4)}-y=3 t+\sin t \) b) \( y^{\prime \prime \prime}-y^{\prime \prime}-y^{\prime}+y=2 e^{-t}+3 \)2 answers -
Solve the problem \[ \begin{array}{l} \frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=0,02 answers -
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Solve the problem \[ \begin{array}{l} \frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}=0,02 answers -
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Solve the differential equation. 4) \( y^{\prime \prime}-4 y^{\prime}+29 y=0 \) A) \( y=C_{1} e^{2 x}+C_{2} e^{5 x} \) B) \( y=e^{-2 x}\left(C_{1} \cos 5 x+C_{2} \sin 5 x\right) \) C) \( y=e^{x}\left(2 answers -
Solve 8) \( y^{\prime \prime}-8 y^{\prime}+52 y=0 \) B) \( y=C_{1} e^{4 x}+C_{2} e^{6 x} \) A) \( y=e^{x}\left(C_{1} \cos 4 x+C_{2} \sin 6 x\right) \) D) \( y=e^{-4 x}\left(C_{1} \cos 6 x+C_{2} \sin 62 answers -
10) \( y^{\prime \prime}+7 y^{\prime}+12 y=2 x \) Find the particular solution. A) \( y=-\frac{7}{72}+\frac{1}{6} x \) B) \( y=\frac{7}{72}+\frac{1}{6} x \) C) \( y=-\frac{1}{6} x \) D) \( y=+\frac{1}2 answers -
12) Find the general solution of the differential equation \( y^{\prime \prime}+4 y^{\prime}+3 y=20 \cos x \). A) \( y=k 1 e^{3 x}+k_{2} e^{x}-4 \sin x+2 \cos x \) B) \( y=k_{1} e^{-3 x}+k_{2} e^{-x}-2 answers -
por \( S(a+i b)=\left(\begin{array}{cc}a & -b \\ b & a\end{array}\right) \), con. \( a b \in R \) verilica que \( S \) es \( R \)-lineal si Sees un isomosfismo entre Cy Mat \( (2 \times 2, R) \) \[ \b2 answers -
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(a) \( \ddot{y}+\dot{y}-6 y=0 \quad y(0)=1, \dot{y}(0)=0 \) \[ y=C_{1} e^{2 t}+C_{2} e^{-3 t}, C_{1}=\frac{3}{5}, C_{2}=\frac{2}{5} \]2 answers -
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Demuestre que si G 1 y G 2 son grupos abelianos, entonces el producto directo G 1 x G 2 es abeliano.0 answers
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Sin calificar Usar el método de Transformada de Laplace para hallar la solución general de este problema de valor inicial. \[ x^{\prime \prime}+3^{2} x=\sin (2 t) \quad x(0)=0 \quad, x^{\prime}(0)=02 answers