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### Topics - Victor Ivrii

Pages:  2 3 ... 55
1
##### Final Exam / Ab solutely no posting before my command
« on: December 21, 2019, 06:31:02 AM »
All posts removed. Users who made them are not allowed to post on forum

2
##### Term Test 2 / You may post solutions
« on: November 19, 2019, 04:25:47 AM »
After an (almost) perfect solution is posted, no need to post the same solution

3
##### Term Test 2 / Problem 4 (noon)
« on: November 19, 2019, 04:24:35 AM »
Find the general real solution to
$$\mathbf{x}'=\begin{pmatrix} 1 & 3\\ -2 &-3\end{pmatrix}\mathbf{x}$$
and sketch trajectories.

4
##### Term Test 2 / Problem 4 (morning)
« on: November 19, 2019, 04:23:46 AM »
Find the general real solution to
$$\mathbf{x}'=\begin{pmatrix} 2 & -3\\ 4 &-2\end{pmatrix}\mathbf{x}$$
and sketch trajectories.

5
##### Term Test 2 / Problem 4 (main sitting)
« on: November 19, 2019, 04:23:20 AM »
Find the general real solution to
$$\mathbf{x}'=\begin{pmatrix} 3 & 3\\ -2 &-1\end{pmatrix}\mathbf{x}$$
and sketch trajectories.

6
##### Term Test 2 / Problem 3 (noon)
« on: November 19, 2019, 04:22:43 AM »
(a) Find the general solution of
$$\mathbf{x}'=\begin{pmatrix} 1 &2\\ 1 &0\end{pmatrix}\mathbf{x}$$
and sketch trajectories.

(b) Find the general solution
$$\mathbf{x}'=\begin{pmatrix} 1 &2\\ 1 &0\end{pmatrix}\mathbf{x}+ \begin{pmatrix} 0 \\[1pt] \dfrac{6 e^{3t }}{e^{2t}+1}\end{pmatrix}.$$

7
##### Term Test 2 / Problem 3 (morning)
« on: November 19, 2019, 04:21:57 AM »
(a) Find the general solution of
$$\mathbf{x}'=\begin{pmatrix} -2 &1\\ -1 &0\end{pmatrix}\mathbf{x}$$
and sketch trajectories.

(b) Find the general solution
$$\mathbf{x}'=\begin{pmatrix} -2 &1\\ -1 &0\end{pmatrix}\mathbf{x}+ \begin{pmatrix} 0 \\ \dfrac{e^{-t}} {t^2+1} \end{pmatrix}.$$

8
##### Term Test 2 / Problem 3 (main sitting)
« on: November 19, 2019, 04:21:01 AM »
(a) Find the general solution of
$$\mathbf{x}'=\begin{pmatrix} 1 &1\\ -2 &4\end{pmatrix}\mathbf{x}$$
classify fixed point $(0,0)$ and sketch trajectories.

(b) Find the general solution
$$\mathbf{x}'=\begin{pmatrix} 1 &1\\ -2 &4\end{pmatrix}\mathbf{x}+ \begin{pmatrix} \dfrac{e^{4t }}{e^{2t}+1} \\ 0\end{pmatrix}.$$

9
##### Term Test 2 / Problem 2 (noon)
« on: November 19, 2019, 04:19:53 AM »
Consider equation
\begin{equation}
y'''+y''+4y'+4y=-24e^{-2t}.
\label{2-1}
\end{equation}
(a) Write a differential equation for Wronskian of $y_1,y_2,y_3$, which are solutions for homogeneous equation and solve it.

(b) Find fundamental system $\{y_1,y_2,y_3\}$ of solutions for homogeneous equation, and find their Wronskian. Compare with (a).

(c) Find the general solution of (\ref{2-1}).

10
##### Term Test 2 / Problem 2 (morning)
« on: November 19, 2019, 04:18:46 AM »
Consider equation
\begin{equation}
y'''-2y''+4y'-8y=15\cos (t).
\label{2-1}
\end{equation}
(a) Write a differential equation for Wronskian of $y_1,y_2,y_3$, which are solutions for homogeneous equation and solve it.

(b) Find fundamental system $\{y_1,y_2,y_3\}$ of solutions for homogeneous equation, and find their Wronskian. Compare with (a).

(c) Find the general solution of (\ref{2-1}).

11
##### Term Test 2 / Problem 2 (main sitting)
« on: November 19, 2019, 04:17:26 AM »
Consider equation
\begin{equation}
y'''+4y''+y'-6y=24e^{t}.
\label{2-1}
\end{equation}
(a) Write a differential equation for Wronskian of $y_1,y_2,y_3$, which are solutions for homogeneous equation and solve it.

(b) Find fundamental system $\{y_1,y_2,y_3\}$ of solutions for homogeneous equation, and find their Wronskian. Compare with (a).

(c) Find the general solution of (\ref{2-1}).

12
##### Term Test 2 / Problem 1 (noon)
« on: November 19, 2019, 04:15:32 AM »
(a) Find the general solution of
$$y''-3y'+2y=\frac{e^{3t}}{e^{2t}+1}.$$

(b) Find solution satisfying
$$y(0)=y'(0)=0.$$

13
##### Term Test 2 / Problem 1 (morning)
« on: November 19, 2019, 04:14:47 AM »
(a) Find the general solution of
$$y''-y=\frac{12}{e^{t}+1}.$$

(b) Find solution satisfying
$$y(0)=y'(0)=0.$$

14
##### Term Test 2 / Problem 1 (main sitting)
« on: November 19, 2019, 04:13:51 AM »
(a) Find the general solution of
$$y''+4y=\frac{1}{\cos^2(t)},\qquad -\frac{\pi}{2}<t<\frac{\pi}{2}.$$

(b) Find solution satisfying
$$y(0)=y'(0)=0.$$

15
##### Term Test 1 / Problem 4 (afternoon)
« on: October 23, 2019, 06:27:03 AM »
(a) Find the general solution for equation
\begin{equation*}
y'' +2y' +17 y =40 e^{x} +130\sin(4x) .
\end{equation*}
(b) Find solution, satisfying $y(0)=0$, $y'(0)=0$.

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