Advanced Math Archive: Questions from August 13, 2022
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\[ f(x)=\frac{4 \cdot}{s^{3}-84+13} \] (a) \( f(t)=4 e^{3 n} \operatorname{ers} 2 t+7 e^{3 n} \sin 2 t \) (b) \( f(t)=2 e^{m} \) arm \( 2 t+4 e^{m} \sin 24 \) (d) \( f(t)=2 e^{k t} \cos 2 t+6 e^{k t}1 answer -
Solve: \[ y^{\prime \prime}+y=g(x) \] here \( y(0)=0, y^{\prime}(0)=1 \) \[ \mathrm{g}(\mathrm{x})=\left\{\begin{array}{cc} 1 & 0 \leq x3 answers -
Solve: \[ y^{\prime \prime}+4 y^{\prime}+6 y=\sin x, y(0)=1, y^{\prime}(0)=0 \] using Laplace transforms.1 answer -
(a) Find: \[ L^{-1}\left\{\frac{s e^{-s}}{s^{2}-5 s+14}\right\} \] (b) Find: \[ L\left\{t e^{-3 t} \sin 6 t\right\} \]1 answer -
be a function of the real variable, such that: f(x)=4(x-1) determine: f^-1
Sean una funciĆ³n de variable real, tal que: \[ f(x)=4(x-1) \] Determine \( f^{-1} \) a. \( f^{-1}(x)=4 x-1 \) b. \( f^{-1}(x)=\frac{x+4}{4} \) c. \( f^{-1}(x)=\frac{x+2}{3} \) d. \( f^{-1}(x)=4 x-4 \1 answer -
(a) \( y^{\prime \prime}+4 y^{\prime}+3 y=3 x, \quad y(0)=2, \quad y^{\prime}(0)=-1 \). (b) \( y^{\prime \prime}-4 y^{\prime}+4 y=\cos (x), \quad y(0)=3, \quad y^{\prime}(0)=0 \). (c) \( y^{\prime \pr2 answers