General solution for system of differential equations?

[engineertobe]

Consider the system of two masses and three springs shown in the figure

​

​

​

with the following equations of motion:

m1x

=−(k1+k2)x+k2y​

m2y

=k2x−(k2+k3)y​

​

and the following masses and spring constants

m1=4

m2=4

k1=4

k2=8

k3=4

​

Find the general solution of the above system using the given masses and spring constants by solving the system and applying the initial conditions

x(0)=A​

,

x

(0)=B​

,

y(0)=C​

and

y

(0)=D​

.

I got the roots -10 and 1 from r^2+9x-10 and then when I solve for the constants I am getting the wrong answer. DId I get the wrong roots or am I going wrong solving for the constants?

 

[jhonmorkel02]

If a specific ordinary differential equation (3) can be integrated in closed form (see Integration of differential equations in closed form), then it is often possible to obtain relations of the type (4), where the parameters arise as integration constants and are arbitrary. (It is therefore often said that the general solution of an

-th order equation contains arbitrary constants.) However, such a relation is far from always being the general solution in the whole domain of existence and uniqueness of the solution of the Cauchy problem for the original equation.

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