Chapter 4: Q6E (page 164)

Question: Find a general solution to the given differential equation.
$y'' - 5 y' + 6 y = 0$

Short Answer

Expert verified

Answer

The general solution of the given equation is

$y = c_{1} e^{2 t} + c_{2} e^{3 t} .$

Step by step solution

Write the auxiliary equation of the given differential equation

Solve the auxiliary equation,

$m^{2} - 5 m + 6 = 0 m^{2} - 3 m - 2 m + 6 = 0 m (m - 3) - 2 (m - 3) = 0 (m - 2) (m - 3) = 0$

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

Write the general solution.

If an auxiliary equation has distinct real roots as&, then the general solution is given as;

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

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

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Question: Find a general solution to the given differential equation.
$y'' - 5 y' + 6 y = 0$

Short Answer

Step by step solution

Write the auxiliary equation of the given differential equation

Write the general solution.

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Question: Find a general solution to the given differential equation.y''-5y'+6y=0

Short Answer

Step by step solution

Write the auxiliary equation of the given differential equation

Write the general solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Decision Maths

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Question: Find a general solution to the given differential equation.
$y'' - 5 y' + 6 y = 0$