Web bonus problem--Week 3

[Catherine Yue]

a. y=sint/3+c/(sint)^2
b. y=sint/3
c. y=sint/3

[Tiange Gao]

The attached is my solution. Thank you

[Kaiying Jiang]

The final answer is:(detail steps are in attachment)
a. y=1/3*sint+c*[sin(t)]^(-2)
b. When c=0, y=1/3*sin(t)
c. When y=1/3*sin(t), definable on negative infinity to positive infinity, and periodic of 2∏, which is 2 times of Pi.

[Shirley Wen]

[Kaiying Jiang]

[Zhiman Tang]

[Yilin Ye]

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)

[Shiyi Hou]

[Yuming Song]

[Jiayun Huang]

[Ge Shi]

[Yatong Yu]

[Ge Shi]

I already uploaded my solution in reply#30. Sorry for posting the message twice...

[Jiayuwjy Wu]

[Roberto Hechen]