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Messages - annielam

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Term Test 1 / Re: Problem 1 (main sitting)
« on: October 23, 2019, 04:15:46 PM »
Question 1:

a) Find the integrating find and a general solution.


$\mu=e^{\int R_2dx}=e^x$

Multiply $\mu$ to both sides
Since $M_y=N_x$, $x$ is the integrating factor.


$\therefore e^xy+3y^2e^{3x}+(e^x+2ye^{3x})=C$

b) Find a solution where $y(0)=1$
Sub $y(0)=1$
$\therefore e^xy+3y^2e^{3x}+(e^x+2ye^{3x})=7$

Quiz-4 / TUT0302
« on: October 18, 2019, 02:12:38 PM »
Find General Solution:


$y_{p}(t)=Ae^{-t} \Rightarrow Ate^{-t} \Rightarrow At^2e^{-t}$
$            =$





Quiz-3 / TUT0302
« on: October 11, 2019, 02:00:15 PM »
Find the Wronskian of two solutions of the given differential equation.


$=cexp(-\int \frac{1}{x}dx)$


Quiz-2 / TUT0302
« on: October 04, 2019, 02:01:09 PM »
Problem: Show that the given equation becomes exact when multiplied by the integrating factor and solve the equation.

$My=x^{2}3y^{2} \neq Nx=\frac{1}{2}x^{2}$
Therefore it is not exact.

Multiply $\mu(\frac{1}{xy^{3}})$ to both side:
$My=0 = Nx=0$
Now it is exact.

Integrate M with respect to $x$ we get:
Take derivative with respect to $y$ on both side:
$\phi y=N=0+h'(y)$
So $h'(y)=(\frac{1}{y^{3}}+\frac{1}{y})$
$h(y)=\int y^{-3}+y^{-1}dy$

General Solution: $\frac{1}{2}x^{2}-\frac{1}{4}y^{-4}+lny=C$

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