Find the complementary solution of the queation. The given differential equation is:\[\frac{d^3y}{dx^3} - 4\frac{d^2y}{dx^2} + \frac{dy}{dx} + 26 = x^3 - 3\]This is a third-order linear differential equation, where:- $\frac{d^3y}{dx^3}$ is the third derivative of $y$ with respect to $x$.- $\frac{d^2y}{dx^2}$ is the second derivative of $y$ with respect to $x$.- $\frac{dy}{dx}$ is the first derivative of $y$ with respect to $x$.- The terms on the left side represent the differential operator acting on $y$.- The right side, $x^3 - 3$, is a polynomial function of $x$. This equation could be used to model phenomena in various fields such as physics or engineering where third-order processes are involved.

Name: Find the complementary solution of the queation. The given differentia
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: Find the complementary solution of the queation. The given differential equation is:\[\frac{d^3y}{dx^3} - 4\frac{d^2y}{dx^2} + \frac{dy}{dx} + 26 = x^3 - 3\]This is a third-order linear differential equation, where:- $\frac{d^3y}{dx^3}$ is the thir

given differential equation isd3ydx3-4d2ydx2+dydx+26=x3-3for complemantry solution of given…

Answered: d³y d²y, dy 4- + + 26 = x3 – 3 dx3 dx²…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

Find the complementary solution of the queation.

The given differential equation is:

\[
\frac{d^3y}{dx^3} - 4\frac{d^2y}{dx^2} + \frac{dy}{dx} + 26 = x^3 - 3
\]

This is a third-order linear differential equation, where:
- $\frac{d^3y}{dx^3}$ is the third derivative of $y$ with respect to $x$.
- $\frac{d^2y}{dx^2}$ is the second derivative of $y$ with respect to $x$.
- $\frac{dy}{dx}$ is the first derivative of $y$ with respect to $x$.
- The terms on the left side represent the differential operator acting on $y$.
- The right side, $x^3 - 3$, is a polynomial function of $x$.

This equation could be used to model phenomena in various fields such as physics or engineering where third-order processes are involved.

Expert Solution

Step 1

$g i v e n d i f f e r e n t i a l e q u a t i o n i s \frac{d^{3} y}{d x^{3}} - 4 \frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} + 26 = x^{3} - 3 f o r c o m p l e m a n t r y s o l u t i o n o f g i v e n d i f f e r e n t i a l e q u a t i o n \frac{d^{3} y}{d x^{3}} - 4 \frac{d^{2} y}{d x^{2}} + \frac{d y}{d x} + 26 = 0 w e t a k e \frac{d^{n} y}{d x^{n}} = m^{n} f r o m g i v e n d i f f e r e n t i a l e q u a t i o n, w e g e t m^{3} - 4 m^{2} + m + 26 = 0 n o w f a c t o r i z e t h e e q u a t i o n (m + 2) (m^{2} - 6 m + 13) = 0 \Rightarrow m + 2 = 0 \Rightarrow m = - 2 \Rightarrow m^{2} - 6 m + 13 = 0 m = \frac{- 6 \pm \sqrt{36 - 52}}{2} = \frac{- 6 \pm 4 i}{2} = - 3 \pm 2 i$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Sequence$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions