Chapter 1: Q25P (page 1)

Find the general solutions of the following equations and compare computer solutions.
$(D^{3} + D^{2} - 6 D) y = 0$

Short Answer

Expert verified

The general solution is. $y = c_{1} + c_{2} e^{- 3 x} + c_{3} e^{2 x}$

Step by step solution

Given information from question

Given equation is. $(D^{3} + D^{2} - 6 D) y = 0$ $(D^{3} + D^{2} - 6 D) y = 0$ $(D^{3} + D^{2} - 6 D) y = 0$

Differential equation

A differential equation is a formula that connects the derivatives of one or more unknown functions. Functions are used to represent physical quantities, derivatives are used to characterise their rates of change, and differential equations are used to define a relationship between them in applications.

Calculate the general solution of(D3+D2−6D)y=0

The auxiliary equation is,

$\begin{array}{l} (D^{3} + D^{2} - 6 D) y = 0 \\ D (D + 3) (D - 2) y = 0 \end{array}$

It is found that the general solution for any differential that has an auxiliary equation with unequal roots is

$y = c_{1} e^{a_{1} x} + c_{2} e^{a_{2} x} + \dots .. + c_{n} e^{a_{n} x}$

Where in our cases. $a_{1} = 0, a_{2} = - 3, a_{3} = 2$

Then,the differential equation's generic solution is, $y = c_{1} + c_{2} e^{- 3 x} + c_{3} e^{2 x}$

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Find the general solutions of the following equations and compare computer solutions.
$(D^{3} + D^{2} - 6 D) y = 0$

Short Answer

Step by step solution

Given information from question

Differential equation

Calculate the general solution of(D3+D2−6D)y=0

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Find the general solutions of the following equations and compare computer solutions.(D3+D2−6D)y=0

Short Answer

Step by step solution

Given information from question

Differential equation

Calculate the general solution of(D3+D2−6D)y=0

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Nuclear Physics

Rotational Dynamics

Measurements

Solid State Physics

Medical Physics

Physics of Motion

Study anywhere. Anytime. Across all devices.

Find the general solutions of the following equations and compare computer solutions.
$(D^{3} + D^{2} - 6 D) y = 0$