Show that the given function is a solution of the differential equation. d²y dy dx dx² dx d²y dx² Substituting checks. d²y dy dx²¹ 8x -7x - 56y= 0, y = c₁e³x + c₂е¯ and y into the original equation gives - 56(c₁e³x + c₂e-7x) = 0. The solution
Show that the given function is a solution of the differential equation. d²y dy dx dx² dx d²y dx² Substituting checks. d²y dy dx²¹ 8x -7x - 56y= 0, y = c₁e³x + c₂е¯ and y into the original equation gives - 56(c₁e³x + c₂e-7x) = 0. The solution
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
Show that the given function is a solution of the
*** Please see attachment
![**Verify the Solution of the Differential Equation**
**Problem Statement:**
Show that the given function is a solution of the differential equation.
**Equation:**
\[
\frac{d^2y}{dx^2} - \frac{dy}{dx} - 56y = 0, \quad y = c_1 e^{8x} + c_2 e^{-7x}
\]
**Solution Steps:**
1. **First Derivative:**
\(\frac{dy}{dx} = \Box\)
2. **Second Derivative:**
\(\frac{d^2y}{dx^2} = \Box\)
3. **Substitution:**
Substitute \(\frac{d^2y}{dx^2}\), \(\frac{dy}{dx}\), and \(y\) into the original equation:
\(\Box - 56(c_1 e^{8x} + c_2 e^{-7x}) = 0\).
The solution checks.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50b7307d-f147-4c39-812e-01e48cbfa721%2F071fa6a0-7b5a-4837-b747-ec32f701c469%2Fif3pp8o_processed.png&w=3840&q=75)
Transcribed Image Text:**Verify the Solution of the Differential Equation**
**Problem Statement:**
Show that the given function is a solution of the differential equation.
**Equation:**
\[
\frac{d^2y}{dx^2} - \frac{dy}{dx} - 56y = 0, \quad y = c_1 e^{8x} + c_2 e^{-7x}
\]
**Solution Steps:**
1. **First Derivative:**
\(\frac{dy}{dx} = \Box\)
2. **Second Derivative:**
\(\frac{d^2y}{dx^2} = \Box\)
3. **Substitution:**
Substitute \(\frac{d^2y}{dx^2}\), \(\frac{dy}{dx}\), and \(y\) into the original equation:
\(\Box - 56(c_1 e^{8x} + c_2 e^{-7x}) = 0\).
The solution checks.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
