Sample Solution from
A First Course in Differential Equations with Modeling Applications (MindTap Course List)
11th Edition
ISBN: 9781305965720
Chapter 1
Problem 1RE
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Textbook Problem

In Problems 1 and 2 fill in the blank and then write this result as a linear first-order differential equation that is free of the symbol c1 and has the form dy/dx = f(x, y). The symbol c1 represents a constant.

d d x c 1 e 10 x = _ _ _ _ _ _

Expert Solution
To determine

To fill: The blank in the statement “ddx(c1e10x)= _______.

Answer

The completed statement is “ddx(c1e10x)=10y_ where y=c1e10x.

Explanation of Solution

Procedure used:

Formation to a linear first order differential equation:

Begin with considering the case of a linear firs-order differential equation ddx(ceax), where y=c1eax, a is constant. Differentiate the linear firs-order differential equation ddx(ceax) becomes,

ddx(ceax)=aceaxdydx=ya

Calculation:

The given differential equation is, ddxc1e10x.

Differentiate the differential equation ddxc1e10x with respect to x.

ddx(c1e10x)=10c1e10xdydx=10y

Hence, the completed statement is “ddx(c1e10x)=10y_ where y=c1e10x.

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