7. For the differential equation (12x)y" + 2y' + (2x - 3)y=e=" (a) Write the associated homogeneous equation and check that y₁(x) = e and y₂(x) = xe are linearly independent solutions of the associated equations. (b) Check that yp(x) = −e-ª is a solution of the full equation. (c) Use superposition principle to write down the general solution of the full equation.
7. For the differential equation (12x)y" + 2y' + (2x - 3)y=e=" (a) Write the associated homogeneous equation and check that y₁(x) = e and y₂(x) = xe are linearly independent solutions of the associated equations. (b) Check that yp(x) = −e-ª is a solution of the full equation. (c) Use superposition principle to write down the general solution of the full equation.
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
100%
For the differential equation (1 − 2x)y'' + 2y' + (2x − 3)y = e−x
(a) Write the associated homogeneous equation and check that y1(x) = e x and y2(x) = xe−x are two linearly independent solutions of the associated equations.
(b) Check that yp(x) = − 1/4 e−x is a solution of the full equation.
(c) Use superposition principle to write down the general solution of the full equation.
(d) Use the existence theorem or the Wronskian to find the intervals on which the solution is valid.
Transcribed Image Text:7. For the differential equation (12x)y" + 2y' + (2x - 3)y = e
(a) Write the associated homogeneous equation and check that y₁(x) = eª and y₂(x) = xe are two
linearly independent solutions of the associated equations.
(b) Check that yp(x) = -e-² is a solution of the full equation.
(c) Use superposition principle to write down the general solution of the full equation.
(d) Use the existence theorem or the Wronskian to find the intervals on which the solution is valid.
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 3 steps with 3 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,
