Chapter 4: Q2E (page 164)

Question: Find a geneQuestion: Find a general solution to the given differential equation.ral solution to the given differential equation.
$y'' + 6 y' + 9 y = 0$

Short Answer

Expert verified

Answer

The general solution of the given equation is $y = c_{1} e^{- 3 t} + c_{2} {te}^{- 3 t} .$

Step by step solution

Write the auxiliary equation of the given differential equation.

The differential equation is $y'' + 6 y' + 9 y = 0 .$ $y'' + 6 y' + 9 y = 0 .$

The auxiliary equation for the above equation $m^{2} + 6 m + 9 = 0 .$

Find the roots of the auxiliary equation.

Solve the auxiliary equation,

$m^{2} + 6 m + 9 = 0 m^{2} + 3 m + 3 m + 9 = 0 m (m + 3) + 3 (m + 3) = 0 (m + 3) (m + 3) = 0$

The roots of the auxiliary equation are $m_{1} = - 3, & m_{2} = - 3 .$

If the auxiliary equation has repeated real roots, then the general solution is given as;

$y = c_{1} e^{m_{1} t} + c_{2} {te}^{m_{2} t}$

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Question: Find a geneQuestion: Find a general solution to the given differential equation.ral solution to the given differential equation.
$y'' + 6 y' + 9 y = 0$

Short Answer

Step by step solution

Write the auxiliary equation of the given differential equation.

Find the roots of the auxiliary equation.

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Question: Find a geneQuestion: Find a general solution to the given differential equation.ral solution to the given differential equation.y''+6y'+9y=0

Short Answer

Step by step solution

Write the auxiliary equation of the given differential equation.

Find the roots of the auxiliary equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Decision Maths

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Question: Find a geneQuestion: Find a general solution to the given differential equation.ral solution to the given differential equation.
$y'' + 6 y' + 9 y = 0$