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Topics - Victor Ivrii

Pages: [1] 2 3 ... 55
1
Test 2 / Misprints are possible
« on: March 30, 2022, 07:17:41 PM »
Misprints are possible

2
Chapter 3 / MOVED: Chapter 4.2, Example 6
« on: February 14, 2022, 07:10:42 AM »

3
Chapter 3 / MOVED: S2.2 Q1
« on: February 02, 2022, 06:22:00 PM »

4
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

5
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

6
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.

7
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.

8
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.

9
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
$$\mathbf{x}'=\begin{pmatrix} 1 &2\\ 1 &0\end{pmatrix}\mathbf{x}+ \begin{pmatrix} 0 \\[1pt] \dfrac{6 e^{3t }}{e^{2t}+1}\end{pmatrix}.$$

10
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
$$\mathbf{x}'=\begin{pmatrix} -2 &1\\ -1 &0\end{pmatrix}\mathbf{x}+ \begin{pmatrix} 0 \\ \dfrac{e^{-t}} {t^2+1} \end{pmatrix}.$$

11
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
$$\mathbf{x}'=\begin{pmatrix} 1 &1\\ -2 &4\end{pmatrix}\mathbf{x}+ \begin{pmatrix} \dfrac{e^{4t }}{e^{2t}+1} \\ 0\end{pmatrix}.$$

12
Term Test 2 / Problem 2 (noon)
« on: November 19, 2019, 04:19:53 AM »
Consider equation

y'''+y''+4y'+4y=-24e^{-2t}.
\label{2-1}

(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}).

13
Term Test 2 / Problem 2 (morning)
« on: November 19, 2019, 04:18:46 AM »
Consider equation

y'''-2y''+4y'-8y=15\cos (t).
\label{2-1}

(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}).

14
Term Test 2 / Problem 2 (main sitting)
« on: November 19, 2019, 04:17:26 AM »
Consider equation

y'''+4y''+y'-6y=24e^{t}.
\label{2-1}

(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}).

15
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
$$y(0)=y'(0)=0.$$

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