Concept explainers
a.
To fill: The blank in the statement “An equation that involves an unknown function and its derivatives is called a/an ______” with the appropriate answer.
a.
Answer to Problem 1CRQ
The completed statement is “An equation that involves an unknown function and its derivatives is called a
Explanation of Solution
It is known that, “An equation which contains the derivative or differential of an unknown function is said to be a differential function”.
In other words, a differential equation is a relation between an unknown function and derivatives.
Consider a differential equation as,
That is, u is an unknown function that is a dependent variable and x, t are two independent variables.
Hence, “An equation that involves an unknown function and its derivatives is called a
b.
To fill: The blank in the statement “A solution of a differential equation is any function that ____ the differential equation” with the appropriate answer.
b.
Answer to Problem 1CRQ
The completed statement is “A solution of a differential equation is any function that
Explanation of Solution
It is known that, “A solution of a differential equation
Consider a differential equation as,
In order to check whether the solution of the differential equation
Now substitute
Observe that, the left hand side is equal to the right hand side.
Hence, “A solution of a differential equation is any function that
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Chapter 9 Solutions
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