Chapter 4: Q4.3-15E (page 172)

Find a general solution $y'' - 3 y' - 11 y = 0$

Short Answer

Expert verified

The general solution of the given equation $y'' - 3 y' - 11 y = 0$ is $y (t) = c_{1} e^{^{\frac{(3 + \sqrt{53}) t}{}}} + c_{2} e^{\frac{(3 - \sqrt{53}) t}{}}$ .

Step by step solution

Given information.

The differential equation is $y'' - 3 y' - 11 y = 0 .$

Finding roots of the auxiliary equation.

Then the auxiliary equation is $r^{2} - 3 r - 11 = 0 .$

The roots of the auxiliary equation are:

$\begin{matrix} r = \frac{3 \pm \sqrt{3^{2} - 4 \times - 11 \times 1}}{2 \times 1} \\ r = \frac{3 \pm \sqrt{9 + 44}}{2} \\ r = \frac{3 \pm \sqrt{53}}{2} \end{matrix}$

Final answer.

Therefore, the general solution is:

$y (t) = c_{1} e^{^{\frac{(3 + \sqrt{53}) t}{2}}} + c_{2} e^{\frac{(3 - \sqrt{53}) t}{2}}$

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Find a general solution $y'' - 3 y' - 11 y = 0$

Short Answer

Step by step solution

Given information.

Finding roots of the auxiliary equation.

Final answer.

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Find a general solution y''-3y'-11y=0

Short Answer

Step by step solution

Given information.

Finding roots of the auxiliary equation.

Final answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Find a general solution $y'' - 3 y' - 11 y = 0$