Question

y''+9y=1, y(0)=0, y'(pi/2)=3
must be solve by green's function

Answer 1

You could use undetermined coefficients to solve this. Do you know about undetermined coefficients?

Answer 2

i found c1cos3x+c2sin3x but i didn't know how to find c1 and c2

Answer 3

To find \(C_1\) and \(C_2\), simply plug in the initial conditions. Then find the derivative of the solution. And again apply the initial conditions. You sould get a system.

Answer 4

Remember: \(y=y_c+y_p\), you already found you're complimentary solution: \(y_c\), no wyou need to find \(y_p\)

Answer 5

yc=c1cos3x+c2sin3x
yc'=-3c1sin3x+3c2cos3x
y(0)=0 c1=0
y'(pi/2)=3 3c1=3 c1=1????? couldn't find c2

Answer 6

this is a BVP problem and i need to find yc only

Answer 7

y(0)=0 c1=0 then let c2=1 so y1=sin3x is this right?

Answer 8

y'(pi/2)=3 3c1=3 c1=1.......i don't know how to find y2

Answer 9

Wait, hold on, let me do this really quick im getting a paper.

Answer 10

actually the question need to solve by green's function so i gotta find y1 and y2 first

Answer 11

i still think you need to get your particular solution. The solution i got was: \(y = c_1\cos(3x)+c_2\sin(3x)+\frac{ 1 }{ 9 }\)

Answer 12

Plugging in the intial conditions: \[c_1+\frac{ 1 }{ 9 } = 0\]

Answer 13

Actually, I'm getting lost in this myself now. I will respond to you. loL. Give me a minute to figure this one out. Lol

Answer 14

i have to use this formula to solve this question

Answer 15

How is \(G\) relevant?

Answer 16

\[yp(x)=\int\limits_{xo}^{x} G(x,t)f(t)dt\]

Answer 17

\[yp(x)=\int\limits_{a}^{x}\frac{ y1(t)y2(x) }{ w(t)}f(t)dt+\int\limits_{x}^{b}\frac{ y1(x)y2(t) }{w(t)}f(t)dt\]

Answer 18

I would love to help, but I'm extremely confused.

Answer 19

this BVP question gotta be solve by green's function