Concept explainers
In Problems 1 through 16, a homogeneous second-order linear differential equation, two functions
Program Description: Purpose of problem is to verify that
Explanation of Solution
Given information:
The homogeneous second order differential equation is
The value of
The initial condition is
Explanation:
The given differential equation can be represented as,
Substitute
Therefore, it is verified that
Substitute
Therefore, it is verified that
The solution of the differential equation can be written as,
Substitute,
Differentiate equation (3) with respect to x as shown below.
Apply first initial condition
Apply second initial condition
Substitute
Therefore, the value of
Substitute
Conclusion:
Thus, the solution of differential equation
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Chapter 3 Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
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