Advanced Math Archive: Questions from May 03, 2023
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4. Solve the initial value problem \[ y^{\prime \prime}-y=8 e^{-t} \sin (2 t), \quad y(0)=0, \quad y^{\prime}(0)=0 \]2 answers -
Find the general solution of the following differential equations:​​​​​​​
\( \begin{array}{l}y^{(4)}-y^{\prime \prime}=0 \\ y^{(4)}-y=0 \\ y^{\prime \prime \prime}-2 y^{\prime \prime}+y^{\prime}=0 \\ y^{\prime \prime \prime}-3 y^{\prime \prime}+y^{\prime}+y=0 \\ y^{(5)}-y^{2 answers -
Find the solution of the following initial value problems: 4. \( y^{\prime \prime}+2 y^{\prime}-3 y=0, \quad y(0)=1, y^{\prime}(0)=1 \) 5. \( y^{\prime \prime}+4 y^{\prime}+3 y=0, \quad y(0)=3, y^{\pr2 answers -
Find the solution of following intiol volue problems \[ \begin{array}{lll} 1-y^{\prime \prime}+2 y^{\prime}-3 y=0 & y(0)=1 & y^{\prime}(0)=1 \\ 2-y^{\prime \prime}+4 y^{\prime}+3 y=0 & y(0)=3 & y^{\pr2 answers -
2. Find the general solutions of the following ODEs: (a) \( y^{\prime \prime}-6 y^{\prime}+9 y=18 x \) (b) \( y^{\prime \prime}-6 y^{\prime}+9 y=-e^{3 x} \) (c) \( y^{\prime \prime}-6 y^{\prime}+9 y=12 answers -
Componentes del galletero \begin{tabular}{|c|c|c|} \hline Figura & Ecuación & Imagen \\ \hline Esfera \( 5 \mathrm{~cm} \) radio & \( x^{2}+y^{2}+(z-5)^{2}=25 \) \\ \hline Esfera \( 4 \mathrm{~cm} \)0 answers -
Verify each identity. 1. \( \left(\sec ^{2} \theta-1\right) \cos ^{2} \theta=\sin ^{2} \theta \) 2. \( \sec ^{2} \theta\left(1-\cos ^{2} \theta\right)=\tan ^{2} \theta \) 3. \( \sin \theta-\sin \theta2 answers -
Given \( 2 y^{\prime \prime}+y^{\prime}-y=-1, y(0)=1 ; y^{\prime}(0)=2 \). Find \( y^{\prime \prime \prime}(0) \). A. \( 3 / 2 \) B. 1 C. -1 D. \( -3 / 2 \)2 answers -
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Hallar los atwalores y correspondientes autorectores de \( \mathrm{A}=\left[\begin{array}{ll}2 & -2 \\ 1 & 5\end{array}\right] \)2 answers -
\[ " S^{\prime \prime}=\left\{(x, y, z):(3 x)^{2}+z^{2}=y^{2}, 0 \leq y \leq 4\right\} \] Using stoke' Theorem verify \( F(x, y, z)= \) \[ -y i+2 x j+o k \]2 answers -
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\[ 3 x y^{\prime}-2 y=x^{3} y^{-2} \] Como ecuación de Bernoulli a) (3pts) Re-escriba, si es necesario la ecuación como una que cumpla con la definicion de Bernoulli. Luego, identifique: \( P(x), Q(2 answers -
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Considere una particula de masa \( m \) que se encuentra atada a un resorte de largo \( L_{0} y \) constante elástica \( k \), cuyo otro extremo se encuentra fijo. El movimiento de la partÃcula ocur2 answers -
Establish the identity \( \tan (2 \pi-\theta)=-\tan \theta \). Which of the following four statements establishes the identity? A. \[ \tan (2 \pi-\theta)=\frac{\tan 2 \pi-\tan \theta}{1-\tan 2 \pi \ta2 answers