   Chapter 17, Problem 2RE

Chapter
Section
Textbook Problem

Solve the differential equation.2.  2y" – 2y' + 10y =0

To determine

To solve: The differential equation of y2y+10y=0 .

Explanation

Given data:

The differential equation is,

y2y+10y=0 (1)

Formula used:

Write the expression of 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 the complex roots.

r=α±iβ (4)

Here,

α is the real part of the root, and

β is the imaginary part of the root.

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

y=eαx(c1cosβx+c2sinβx) (5)

Write the expression to find the roots of quadratic equation.

r=b±b24ac2a (6)

Compare equations (1) and (2).

a=1b=2c=10

Substitute 1 for a, –2 for b, and 10 for c in equation (3),

(1)r2+(2)r+(10)=0r22r+10=0

Find the roots of auxiliary equation using equation (6)

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