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Topics - Victor Ivrii

Pages: 1 [2] 3 4 ... 36
16
Term Test 1 / P3-Morning
« on: February 15, 2018, 05:12:13 PM »
(a) Find the general solution for equation
\begin{equation*}
y''(t)-5y'(t)+6y(t)=4e^{t}+e^{2t} .
\end{equation*}

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

17
Term Test 1 / P2-Morning
« on: February 15, 2018, 05:10:58 PM »
(a)  Find Wronskian  $W(y_1,y_2)(x)$ of a fundamental set of solutions $y_1(x) , y_2(x)$ for ODE 
\begin{equation*}
-x^2\bigl(\ln(x)-1\bigr)y''+xy'-y=0
\end{equation*}

(b) Check that $y_1(x)=x$ is a solution and find another linearly independent solution.
 
(c) Write the general solution,  and find solution such that ${y(1)=1, y'(1)=0}$.


18
Term Test 1 / P1-Morning
« on: February 15, 2018, 05:09:54 PM »
Find integrating factor and then a general solution of ODE
\begin{equation*}
(4x y^2+3\ln(x)+1)+2x^2yy'=0 \ .
\end{equation*}
 
Also, find a solution satisfying $y(1)=1$.

19
Term Test 1 / P4-Day
« on: February 15, 2018, 05:08:16 PM »
Find the general solution for equation
\begin{equation*}
y''(t)-4y'(t)+5y(t)=2 e^{t}+ 8\cos(t).
\end{equation*}

20
Term Test 1 / P3-Day
« on: February 15, 2018, 05:07:40 PM »
(a) Find the general solution for equation
\begin{equation*}
y''(t)-3y'(t)+2y(t)=-6+3 e^{t} .
\end{equation*}

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

21
Term Test 1 / P2-Day
« on: February 15, 2018, 05:06:52 PM »
(a) Find Wronskian  $W(y_1,y_2)(x)$ of a fundamental set of solutions $y_1(x) , y_2(x)$ for ODE 
\begin{equation*}
\bigl(x^2-1\bigr)y''-2xy'+2y=0
\end{equation*}

(b) Check that $y_1(x)=x$ is a solution and find another linearly independent solution.
 
(c)  Write the general solution,  and find solution such that ${y(0)=1, y'(0)=2}$.


22
Term Test 1 / P1-Day
« on: February 15, 2018, 05:05:37 PM »
Find integrating factor and then a general solution of ODE
\begin{equation*}
2xy +(4x^2+4e^y+ye^y)y'=0 \ .
\end{equation*}
 
Also, find a solution satisfying $y(1)=1$.

23
Term Test 1 / P-4
« on: February 13, 2018, 09:25:55 PM »
Find the general solution for equation
\begin{equation*}
y''(t)+2y'(t)+2y(t)=-e^{-t}+ 10\cos(t).
\end{equation*}

24
Term Test 1 / P-3
« on: February 13, 2018, 09:25:20 PM »
(a) Find the general solution for equation
\begin{equation*}
y''(t)+y'(t)-2y(t)=-6+9 e^{-2t} .
\end{equation*}

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


25
Term Test 1 / P-2
« on: February 13, 2018, 09:24:12 PM »
(a)  Find Wronskian  $W(y_1,y_2)(x)$ of a fundamental set of solutions $y_1(x) , y_2(x)$ for ODE 
\begin{equation*}
\bigl(x\sin(x)+\cos(x)\bigr)y''-x\cos(x)y'+\cos(x)y=0
\end{equation*}
(b) Check that $y_1(x)=x$ is a solution and find another linearly independent solution.
 
(c) Write the general solution,  and find solution such that ${y(0)=1, y'(0)=1}$.


26
Term Test 1 / P-1
« on: February 13, 2018, 09:22:23 PM »
Find integrating factor and then a general solution of ODE
\begin{equation*}
y^2 + (3xy - \cos(y))y' = 0 \ .
\end{equation*}
 
Also, find a solution satisfying $y(1)=\pi$.

27
Quiz-3 / Q3-T5102
« on: February 10, 2018, 06:58:27 PM »
  • Find solution
    \begin{equation*}
    \left\{ \begin{aligned}
    & u_{tt}-c^2u_{xx}=0, &&&t > 0, x > 0,  \\
    &u|_{t=0}= \phi (x),   &&u_t|_{t=0}= c\phi'(x) &x > 0, \\
    &(u_x+\alpha u_{t})|_{x=0}=0,  &&&t > 0
    \end{aligned}
    \right.
    \end{equation*}
    (separately in $x>ct$, and $0<x<ct$).
  • In particular, consider $\phi(x)=e^{ikx}$.

28
Quiz-3 / Q3-T0101
« on: February 10, 2018, 06:57:13 PM »
  • Find solution
    \begin{equation*}
    \left\{ \begin{aligned}
    & u_{tt}-c^2u_{xx}=0, &&&t > 0, x > 0,  \\
    &u|_{t=0}= \phi (x),   &&u_t|_{t=0}= c\phi'(x) &x > 0, \\
    &(u_x+\alpha u)|_{x=0}=0,  &&&t > 0
    \end{aligned}
    \right.
    \end{equation*}
    (separately in $x>ct$, and $0<x<ct$).
  • In particular, consider $\phi(x)=e^{ikx}$.

29
APM346--Misc / MOVED: Tag each equation in an IVP
« on: February 10, 2018, 05:36:32 PM »

30
MAT244--Announcements / Solutions for Quizzes
« on: February 10, 2018, 05:23:21 PM »
Post only solutions for your tutorial section. But you may discuss for any section

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