x" + 2(3+R)x' + 3(3+R)x = 0 - Initial conditions

[markbrock30]

x" + 2*(3+R)*x' + 3*(3+R)*x = 0

x(0) = 10

the above equation (second order) was derived from:

(dx/dt) = -(3+R)*x + R*y, and
(dy/dt) = (3+R)*x - (3+R)*y


How can I find x'(0)?

I can't replicate the examples in my notes.


Cheers,

Mark.

 

[Deleted member 4993]

x" + 2*(3+R)*x' + 3*(3+R)*x = 0

x(0) = 10

the above equation (second order) was derived from:

(dx/dt) = -(3+R)*x + R*y, and
(dy/dt) = (3+R)*x - (3+R)*y


How can I find x'(0)?

I can't replicate the examples in my notes.


Cheers,

Mark.

Let

z= 3+R

then solution of the above equation is:

x = A e^[{-z+(Rz)[sup:27c0gmet]1/2[/sup:27c0gmet]}t] + B e^[{-z-(Rz)[sup:27c0gmet]1/2[/sup:27c0gmet])}t]

proceed from here and show us what you get.

 

[markbrock30]

Nevermind, I figured it out.


Cheers anyway,

Mark.