Answer:
The solution of this differential system is .
Step-by-step explanation:
This second-order differential equation is homogeneous and linear of the form:
(1)
Where:
- First-order constant coefficient, dimensionless.
- Zero-order constant coefficient, dimensionless.
Whose characteristic polynomial is:
(2)
Where contains the roots associated with the solution of the differential equation.
If we know that and , the roots of the characteristic equation are, respectively:
Which means that and the solution of the differential equation is of the form:
(3)
Where and are integration constants.
The first derivative of the equation above is:
(4)
Now, if we get that and , then the system of equations to the solved is:
(3b)
(4b)
The solution of this system is: , . Therefore, the solution of this differential system is .