Solving System of Two Differential Equations

In summary, the conversation discusses finding the general solution of a system of equations involving variables x, y, and t. The individual equations are (2D+5)x - (2D+3)y = t and (D-2)x + (D+2)y = 0. The quadratic formula did not provide any solution, and there is uncertainty about finding the complementary solution. The conversation also mentions the possibility of a wrong characteristic equation and suggests retyping the equations for better clarity.
  • #1
tsslaporte
12
0
Homework Statement

Find General Solution of the Following System

(2D+5)x - (2D+3)y = t

(D-2)x + (D+2)y = 0


https://dl.dropboxusercontent.com/u/32294083/Emath/New%20Doc%203_1.jpg


Using the Quadratic Formula I get nothing so I am not sure what the complementary solution is.

After this what do I do to find the General Solution?
 
Last edited by a moderator:
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  • #2
tsslaporte said:
Homework Statement

Find General Solution of the Following System

(2D+5)x - (2D+3)y = t

(D-2)x + (D+2)y = 0


https://dl.dropboxusercontent.com/u/32294083/Emath/New%20Doc%203_1.jpg


Using the Quadratic Formula I get nothing so I am not sure what the complementary solution is.

After this what do I do to find the General Solution?

Start over: your "characteristic equation" is wrong, so far as I can make out. You really should type this stuff out; your writing is borderline unreadable.
 
Last edited by a moderator:

Related to Solving System of Two Differential Equations

1. What is a system of two differential equations?

A system of two differential equations is a set of two equations that involve one or more variables and their derivatives. These equations describe the relationship between the variables and how they change over time.

2. Why do we need to solve a system of two differential equations?

Solving a system of two differential equations allows us to find the values of the variables that satisfy both equations simultaneously. This can help us understand the behavior of a system and make predictions about its future state.

3. What methods can be used to solve a system of two differential equations?

There are several methods that can be used to solve a system of two differential equations, including elimination, substitution, and the use of matrices. The most appropriate method will depend on the specific equations and their complexity.

4. How do initial conditions affect the solution of a system of two differential equations?

Initial conditions, also known as boundary conditions, are values of the variables at a specific point in time. These conditions are necessary to uniquely determine the solution of a system of two differential equations. Without them, there may be multiple solutions that satisfy the equations.

5. Can a system of two differential equations have a unique solution?

Yes, a system of two differential equations can have a unique solution if there is a one-to-one correspondence between the equations and the unknown variables. This means that each variable has only one derivative in each equation and there are no redundant equations that do not contribute to the solution.

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