2. Use an appropriate method to find the general solution of the following differential equat (a) y" + 3y' – 2y = -e2" (5 cos 2x + 9 sin 2a)
2. Use an appropriate method to find the general solution of the following differential equat (a) y" + 3y' – 2y = -e2" (5 cos 2x + 9 sin 2a)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Pls answer question 2
![1. Suppose m = {0,0,0, 1, –5, 4±3i, 4±3i} are roots of an auxiliary equation. Write down the general solution
of the corresponding homogeneous linear DE if it is
(а)
an equation with constant coefficients,
(b)
a Cauchy-Euler equation.
2.
Use an appropriate method to find the general solution of the following differential equations:
(a) y" + 3y' – 2y = -e2" (5 cos 2x + 9 sin 2x)
(b) x?y" + 15xy' + 58y = 0
(c) y" – y =
1- e-2r
(d) y" – 6y" + 11y' – 6y = e2" (5 – 4x – 32²)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F528dd133-9887-4da3-be06-5c698b89efe6%2F565a946a-34a4-4166-9947-7de17f8e4f38%2Fhtuc8kq_processed.png&w=3840&q=75)
Transcribed Image Text:1. Suppose m = {0,0,0, 1, –5, 4±3i, 4±3i} are roots of an auxiliary equation. Write down the general solution
of the corresponding homogeneous linear DE if it is
(а)
an equation with constant coefficients,
(b)
a Cauchy-Euler equation.
2.
Use an appropriate method to find the general solution of the following differential equations:
(a) y" + 3y' – 2y = -e2" (5 cos 2x + 9 sin 2x)
(b) x?y" + 15xy' + 58y = 0
(c) y" – y =
1- e-2r
(d) y" – 6y" + 11y' – 6y = e2" (5 – 4x – 32²)
![2.
Use an appropriate method to find the general solution of the following differential equations:
/ – 2y = -e2" (5 cos 2x + 9 sin 2x)
2
(b) x?y" + 15xy' + 58y = 0
(c) y" –
- y =
1-e-2r
(d) y" – 6y" + 11y – 6y = e2" (5 – 4x – 32²)
-
3.
Solve the following differential equation subject to the indicated conditions.
y" – y = x + sin x,
y(0) = 1, y'(0) = -3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F528dd133-9887-4da3-be06-5c698b89efe6%2F565a946a-34a4-4166-9947-7de17f8e4f38%2Fu7wkwxr_processed.png&w=3840&q=75)
Transcribed Image Text:2.
Use an appropriate method to find the general solution of the following differential equations:
/ – 2y = -e2" (5 cos 2x + 9 sin 2x)
2
(b) x?y" + 15xy' + 58y = 0
(c) y" –
- y =
1-e-2r
(d) y" – 6y" + 11y – 6y = e2" (5 – 4x – 32²)
-
3.
Solve the following differential equation subject to the indicated conditions.
y" – y = x + sin x,
y(0) = 1, y'(0) = -3
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)