Other Math Archive: Questions from November 27, 2022
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Solve the following ordinary differential equations (ODE's) using Laplace transforms
\( \begin{array}{lll}\ddot{y}+y=\sin 3 t & y_{o}=0 & \dot{y}_{o}=0 \\ 9 \ddot{y}+6 \dot{y}+y=0 & y_{o}=3 & \dot{y}_{o}=1\end{array} \)2 answers -
9. Solve IVP \[ \frac{d^{2} y}{d x^{2}}+14 \frac{d^{y}}{d x}+49 y=0\left\{\begin{array}{l} y(0)=-1 \\ y^{\prime}(0)=1 \end{array}\right. \] 10. Solve IVP \[ \frac{d^{2} y}{d x^{2}}+49 y=0\left\{\begin2 answers -
1. Show that (a) \( \Gamma ; \alpha \models \varphi \) iff \( \Gamma \models(\alpha \rightarrow \varphi) \); and (b) \( \varphi \models \Rightarrow \psi \) iff \( \models(\varphi \leftrightarrow \psi)0 answers -
differential equations
\begin{tabular}{|l|c|} \hline 1 & \( 2 y^{\prime \prime}+3 y^{\prime}-5 y=0 \) \\ \hline 2 & \( x^{3} y^{\prime \prime \prime}+6 y^{\prime}+10 y=e^{x} \) \\ \hline 3 & \( x^{2} y^{\prime \prime}-6 x y2 answers