Advanced Math Archive: Questions from July 28, 2022
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15.) Solve: \( y^{\prime \prime \prime}-4 y^{\prime \prime}-5 y^{\prime}=9+5 x, \quad y(0)=0, y^{\prime}(0)=0 \) and \( y^{\prime \prime}(0)=4 \)1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ \begin{array}{c} y^{(4)}-12 y^{\prime \prime \prime}+36 y^{\prime \prime}=0 \\ y(0)=4, \quad y^{\prime}(0)=15, \quad y^{\prime \prime}(0)=36, \qua1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ \begin{array}{c} y^{\prime \prime \prime}+4 y^{\prime}=0 \\ y(0)=-9, \quad y^{\prime}(0)=-6, \quad y^{\prime \prime}(0)=-12 \end{array} \]1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ \begin{array}{c} y^{(4)}-12 y^{\prime \prime \prime}+36 y^{\prime \prime}=0, \\ y(0)=4, \quad y^{\prime}(0)=15, \quad y^{\prime \prime}(0)=36, \qu1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ \begin{array}{c} y^{\prime \prime \prime}+4 y^{\prime}=0 \\ y(0)=-9, \quad y^{\prime}(0)=-6, \quad y^{\prime \prime}(0)=-12 \\ y(x)= \end{array} \1 answer -
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(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-5 y^{\prime \prime}+6 y^{\prime}=4 e^{x} \] \( y(0)=29, \quad y^{\prime}(0)=22, \quad y^{\prime \prime}(0)=22 \) \[ y(x)=1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}+25 y^{\prime}=0 \] \[ \begin{array}{l} y(0)=9, \quad y^{\prime}(0)=-10, \quad y^{\prime \prime}(0)=100 \\ y(x)= \end{arra1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-7 y^{\prime \prime}+12 y^{\prime}=30 e^{x} \] \[ y(0)=12, y^{\prime}(0)=11, y^{\prime \prime}(0)=30 \text {. } \] \[ y(x)1 answer -
3 answers
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Find \( f(t) \). \[ L^{-1}\left\{\frac{e^{-\pi s}}{s^{2}+1}\right\} \] \[ f(t)=(\quad) \quad) \mathcal{U}(t-() \]1 answer -
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, z=4 y \) and \( x^{2}=64-y \). 1. \( \int_{a}1 answer -
Find the divergence of the vector field. \[ \mathbf{F}(x, y, z)=7 x^{7} \mathbf{i}-7 x y^{7} \mathbf{j} \] \( \operatorname{div} \mathbf{F}(x, y, z)=\frac{7}{8} x^{8} \mathbf{i}-\frac{7}{8} x y^{8} \m1 answer