Concept explainers
Answer Problems 1–10 without referring back to the text. Fill in the blank or answer true or false.
1. The only solution of the initial-value problem
y″ + x2y = 0, y(0) = 0, y′(0) = 0 is __________.
To fill: The blank in the statement, “The only solution of the initial-value problem
Answer to Problem 1RE
The only solution of the initial value problem
Explanation of Solution
Theorem used:
The existence of a Unique Solution:
For a nth order initial value problem
If
Calculation:
Consider the initial value problem
Compare the equation to the standard form of differential equation
Note that,
The initial value
By the existence of unique solution, the general solution of the initial value problem
Therefore, the only solution of the initial value problem
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Chapter 4 Solutions
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
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