General Solution for a 2x2 Matrix Differential Equation

In summary, a general solution is a mathematical expression that represents all possible solutions to a given equation or problem. It differs from a particular solution in that it includes arbitrary constants or parameters that allow for a range of solutions. An example of expressing a general solution is y = x^2 + C for the differential equation dy/dx = 2x, where C is an arbitrary constant. It is important to express the general solution in order to find all possible solutions and gain a comprehensive understanding of the problem. However, there can be limitations to expressing a general solution and it is important to verify its validity for the given problem.
  • #1
Success
75
0
Express the general solution of x'=(2, 9/5, -5/2, -1)x in terms of real-valued functions.

(this is 2x2 matrix, 2 and 9/5 on the left, -5/2 and -1 on the right. The complex roots are (1/2)+(3/2)i and (1/2)-(3/2)i and a=1, b=(3/5)+(3/5)i for the first root. And a=1, b=(3/5)-(3/5)i for the second root. But I don't know how to get the answer.
 
Physics news on Phys.org
  • #2
Never mind. I solved it.
 

FAQ: General Solution for a 2x2 Matrix Differential Equation

What is a general solution?

A general solution is a mathematical expression that represents all possible solutions to a given equation or problem. It includes any arbitrary constants or parameters that allow for a range of solutions.

How is a general solution different from a particular solution?

A particular solution is a specific solution to a given problem, while a general solution is a formula that represents all possible solutions. A particular solution will have specific values for all variables, while a general solution will have arbitrary constants that can take on different values.

Can you provide an example of expressing a general solution?

Sure, for the differential equation dy/dx = 2x, the general solution would be y = x^2 + C, where C is an arbitrary constant. This general solution can represent all possible solutions to the given differential equation.

Why is it important to express the general solution?

Expressing the general solution allows us to find all possible solutions to a given problem or equation. It provides a comprehensive understanding of the problem and allows for further analysis and manipulation of the solution.

Are there any limitations to expressing a general solution?

Yes, there can be limitations to expressing a general solution. In some cases, the general solution may not be able to represent all possible solutions or may not be applicable for certain values of the variables. It is important to check the validity of the general solution for the given problem.

Similar threads

I Fundamental matrix of a second order 2x2 system of ODEs
Replies
2
Views
2K
I Number of solutions to the order of the equation
Replies
2
Views
942
MHB -307.28.1 Find the general solution to the system of DE
Replies
1
Views
3K
General solution vs particular solution
2
Replies
52
Views
3K
MHB -5.5 Solve the matrix equation AX=B to find x and y
Replies
4
Views
3K
General Solution for a 2x2 Matrix with Complex Eigenvalues
Replies
1
Views
1K
MHB -b.2.1.11 Find the general solution y'+y=5sin{2t}
Replies
3
Views
3K
MHB -m30 - 2nd order linear homogeneous ODE solve using Wronskian
Replies
12
Views
3K
I On error estimates of approximate solutions
Replies
1
Views
1K
I Solution of delayed forcing function
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top