   Chapter 17, Problem 2RQ

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.If y1 and y2 are solutions of y" + 6y' + 5y = x, then c1y1 + c2y2 is also a solution of the equation.

To determine

Whether the statement “If y1 and y2 are solutions of y+6y+5y=x , then c1y1+c2y2 is also a solution of the equation” is true or false.

Explanation

Given data:

y+6y+5y=x , c1y1+c2y2 is solution of equation.

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.

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

ay+by+cy=G(x) (3)

Here,

a , b and c are constants, and

G is continuous function.

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

y(x)=yp(x)+yc(x) (4)

Here,

yp is particular solution, and

yc is general solution of complementary equation

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