Advanced Math Archive: Questions from August 01, 2022
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number 3 and show all work please!
1-11 Use power series to solve the differential equation. 1. \( y^{\prime}-y=0 \) 2. \( y^{\prime}=x y \) 3. \( y^{\prime}=x^{2} y \) 4. \( (x-3) y^{\prime}+2 y=0 \) 5. \( y^{\prime \prime}+x y^{\prim1 answer -
help me solve all
\( \langle 1\rangle \) Solve \( y^{\prime \prime}+y=4 \sin t \) \( \langle 2\rangle \) Solve \( x^{2} y^{\prime}+x(x+2) y=e^{2 x} \) \( \) Solve \( y^{\prime \prime}+2 y^{\prime}+y=18 e^{-x} \) \( \3 answers -
\( y^{\prime \prime \prime}-4 y^{\prime \prime}+y^{\prime}+6 y=0 ; \quad y(0)=-1, \quad y^{\prime}(0)=3, \quad y^{\prime \prime}(0)=-3 \)1 answer -
2. Solve the Initial Value Problem: \( y^{\prime \prime \prime}+2 y^{\prime \prime}-5 y^{\prime}-6 y=0 \) given \( y(0)= \) \( y^{\prime}(0)=0 \) and \( y^{\prime \prime}(0)=1 \)1 answer -
true or false?
7.1 ) Let \( y^{i v}+\frac{1}{t} y^{\prime}=g(t) \) Then \( \mathrm{W}\left(\mathrm{y}_{1}, \mathrm{y}_{2}, \mathrm{y}_{3}, \mathrm{y}_{4}\right)=\mathrm{ct} \).1 answer -
2. Solve the Initial Value Problem: \( y^{\prime \prime \prime}+2 y^{\prime \prime}-5 y^{\prime}-6 y=0 \) given \( y(0)= \) \( y^{\prime}(0)=0 \) and \( y^{\prime \prime}(0)=1 \)1 answer -
1 answer
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3. Sea \( T: V \rightarrow W \) una transformación lineal y sea \( S=\left\{v_{1}, v_{2}, \ldots, v_{n}\right\} \) un conjunto de vectores en \( V \). Demuestre que si \( R=\left\{T v_{1}, T v_{2}, \1 answer -
4. Sea \( T: M_{22} \rightarrow M_{22} \) la transformación definida por \( T\left[\begin{array}{cc}x & y \\ z & w\end{array}\right]=\left[\begin{array}{cc}x+y & y+z \\ x+w & y+w\end{array}\right] \)1 answer -
1. Sea \( T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2} \) una transformación lineal. Suponga que la matriz de transformación de \( T \) es \( A_{T}=\left[\begin{array}{cc}2 & -3 \\ -1 & 4\end{array}3 answers -
3. Diagonalize the matrix \( \left[\begin{array}{ll}2 & 3 \\ 4 & 1\end{array}\right] \) if possible.1 answer -
Find the solution \( u(x, y) \) of \[ \left\{\begin{array}{l} u_{x}+\sin (x) u_{y}=y \\ u(x=0, y)=0 . \end{array}\right. \]1 answer