In Problems 1-4, find a general solution
The general solution
Answer to Problem 1RP
Solution:
The general solution of the system is
Here,
Explanation of Solution
Given:
System of differential equations is,
Approach:
Use elimination method for solving algebraic systems.
Step1: Add or subtract the given equations to get an equation in single variable.
Step2: Solve the single variable equation.
Step3: substitute the value of variable obtained in Step2 in other equations to get the values of other unknowns.
Calculation:
Write the system using the operator notation.
Multiply Equation
Subtract Equation
The auxiliary equation of Equation
Roots of Equation
So, the general solution of Equation
Here,
From Equation
Substitute
Integrating both sides with respect to
Therefore, the general solution of the system is
Here,
Conclusion:
Hence, the general solution of the system is
Here,
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Chapter 5 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning