   Chapter 17, Problem 3RQ

Chapter
Section
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The general solution of y" - y = 0 can be written asy = c1 cosh x + c2 sinh x

To determine

Whether the statement “The general solution of yy=0 can be written as y=c1coshx+c2sinhx ” is true or false.

Explanation

Given data:

yy=0 , y=c1coshx+c2sinhx .

Formula used:

Write the general expression for second-order homogeneous linear differential equation as follows.

ay+by+cy=0 (1)

Here,

a , b and c are constants.

Write the expression for solution of second order linear homogeneous differential equation.

y(x)=c1y1(x)+c2y2(x) (2)

Here,

c1 and c2 are constants, and

y1(x) and y2(x) solution of linear homogeneous equation.

Consider the second order differential equation as follows

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