Question

How to solve general solution of the equation :( d square x / dt square) + 2dx/dt + 2x = 0. Help me please..

Answer 1

x''+2x'+2=0

Answer 2

solve the characteristic equation
\[\lambda^2+2 \lambda+2=0 \text{ first } \]

Answer 3

your solutions would be complex

Answer 4

\[\lambda=a+bi \\ \text{ then solution is } \\ x=c_1 e^{at}\cos(bt)+c_2 e^{at} \sin(bt)\]

Answer 5

type-o
\[\lambda=a \pm bi\]

Answer 6

@lyna9021 are you cool?

Answer 7

Then the question ask to solve the equation given that t=0, x=1, and dx/dt=2

Answer 8

ok so it wants us to also find those constants c1 and c2

Answer 9

From the char equation, x I got 0.22 and -2.22

Answer 10

Then what I need to do the next step? What is c1 and c2?

Answer 11

how do you have that
and leave in exact form

Answer 12

take the derivative of x in the first post, you will have 2 equations with c1,c2, solve

Answer 13

did you use the quadratic formula?

Answer 14

fourth post*

Answer 15

Yes

Answer 16

you are going to leave in exact form and simplify as much as you can

Answer 17

oops that is lambda not x

Answer 18

Yes.I got answer is formula

Answer 19

\[\lambda=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

Answer 20

Yes, then I got the answer -0.22 and 2.22

Answer 21

Ohh that is for c1 n c2??

Answer 22

c1,c2 are not the same as lambda

Answer 23

you solve the characteristic equation in order to find c1,c2

Answer 24

Okay.. What did the answer for c1 n c2?

Answer 25

Okay.. What did the answer for c1 n c2?