Question

2nd order ODE problem.

Answer 1

I am doing something stupidly wrong here and I see where it is

Answer 2

I got the characteristic question to be \[r ^{2}-r+4=0\]

Answer 3

No wait r^2-4r+4=0

Answer 4

Nevermind I just realised I am looking at a trinomial. roots will be the same I believe.

Answer 5

you found the solutions yet? @ironictoaster ?

Answer 6

there is only one from what I can tell r=2

Answer 7

Yeah I got that, general solution seems to be y=c1*e^2x+c2*e^2x

Answer 8

Derive that equation and use my initial conditions.

Answer 9

almost from what I can see here, you have to add an additional x to one of them, that's how it works for multiply identical roots.

\[y=\large c_1e^{2x}+c_2xe^{2x} \]

Answer 10

I did not know that. I've never done question that had double roots.

Answer 11

So that derived would be y'=2c1e^2x+2c1xe^2x

Answer 12

I really should learn latex..

Answer 13

I would first set f(0)=1 that leads to c_1 =1 right?

Answer 14

so you can forget about that constant there.

Answer 15

Sorry the second constant should be c\[_{2}\]

Answer 16

\[c_{2}\]

Answer 17

I get the following as a derivative

\[\Large y'=c_12e^{2x}+ c_2e^{2x}+c_22xe^{2x} \]

Answer 18

Yeah I got the same, I just pulled out the 2's in front of the terms.

Answer 19

got, so you can now substitute your initial conditions and you are done, from y(0) follows directly that c_1 = 1 from what I see, so I would use that to your advantage

Answer 20

Yeah I am left with two similtanous equations. to solve for c1 and c2

Answer 21

\[c_{1}+c _{2}=1\]

\[2c _{1}+c _{2}=4\]

Answer 22

2c1+2c2=4***

Answer 23

I don't think this can be done, everything just cancels out....

Answer 24

the first one doesn't seem correct to me, if you substitute y(0) you are left with c_1=1

Answer 25

\[ y=\large c_1e^{2x}+c_2xe^{2x}\ \\ y(0)=c_1=1\]

Answer 26

second term includes an additional x, therefore it falls away

Answer 27

Awh I forgot to add in the x when writing the equation down. Yeah multiplying by 0 cancels the terms out.

Answer 28

the 2nd term that is

Answer 29

got it?

Answer 30

Yeah the missing x was screwing me up, thanks for the help, the little mistakes will be the end of me!

Answer 31

hehe okay great!