   Chapter 17, Problem 1RE

Chapter
Section
Textbook Problem

Solve the differential equation.1. 4y" – y =0

To determine

To solve: The differential equation of 4yy=0 .

Explanation

Given data:

The differential equation is,

4yy=0 (1)

Formula used:

Write the expression for a second order differential equation.

ay+by+cy=0 (2)

Write the expression for a second order auxiliary equation.

ar2+br+c=0 (3)

Write the expression for general solution of ay+by+cy=0 with two distinct real roots.

y=c1er1x+c2er2x (4)

Here,

r1 and r2 are the roots of the auxiliary equation.

Compare equations (1) and (2).

a=4b=0c=1

Substitute 4 for a, 0 for b, and –1 for c in equation (3),

(4)r2+(0)r+(1)=0

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