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Messages - Yilin Ye

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1
Home Assignment 5 / Re: Problem 1
« on: February 22, 2019, 12:41:09 AM »
(*)should be
𝑢(𝑥,𝑡)=

\begin{matrix} \frac{1}{4\sqrt{kt\pi}}\int_{0}^{inf} exp(-(x-y)^2/4kt)exp(-ay)\, dy\end{matrix}+\begin{matrix}\frac{1}{4\sqrt{kt\pi}} \int_{-inf}^{0} exp(-(x-y)^2/4kt)exp(ay)\, dy\end{matrix}
 

2
Home Assignment 3 / S2.3 problem2(17)(18)
« on: January 30, 2019, 11:49:08 PM »
Do we need to consider all situations when calculating   
\begin{matrix}\frac{1}{2} \int_{x-ct}^{x+ct} h(x)\, dx\end{matrix}

Like
(1) x-ct,x+ct >1
(2)x+ct>1, x-ct<1
(3) -1<x-ct<x+ct<1
(4)-1<x+ct<1,x-ct<-1
(5)x-ct,x+ct<-1

3
Web Bonus Problems / Re: Web bonus problem--Week 3
« on: January 22, 2018, 11:04:08 PM »
a)
y′+2cot(t)y=cos(t).
p(t)=2cot(t)
I=e^∫2cot(t)dt
 =e^2∫cos(t)/sin(t)dt
 =e^2ln|sin(t)|
 =e^ln|sin(t)|^2
 =sin(t)^2

sin(t)^2y′+2cot(t)sin(t)^2y=cos(t)sin(t)^2

(sin(t)^2y)'=cos(t)sin(t)^2
sin(t)^2y=∫cos(t)sin(t)^2dt
              =1/3sin(t)^3+c
            y=1/3sin(t)+csin(t)^-2

b)let c=0  y=1/3sin(t)
c)let c=0  y=1/3sin(t)

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