Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
22d+ + y² = xy (Bernoulli DE)

22d+ + y² = xy (Bernoulli DE)

Advanced Engineering Mathematics
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
icon
Related questions
Question

Can you solve this using the flow given for bernoulli 

Bernoulli's Equation Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it into a linear equation. In this case, we can solve such equation by means of integrating factor method. The most important such equation has the form dy dx (3) where n € R, called the Bernoulli's equation or Bernoulli DE. If n = 0 or n = 1, then (3) is linear. Method of Solution: For n #1 If we multiply both sides of (3) by y", it becomes Let uy-n. Then = + R(x)y = S(x)y" du (1-n)y". da Multiply both sides of (4) by (1-n). = - dy dx 1-n +y¹-"R(x) = S(x) dy dx dy (1-n)y " +(1-n)y¹ R(x) = (1-n)S(x) dx The Bernoulli differential equation is now transformed into the form du +(1-n)R(x) u = (1-n)S(x) dx The above equation is now linear in u and can be solved by integrating factor method. du (6) d.x + P(x) u = f(x)
Transcribed Image Text:Bernoulli's Equation Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it into a linear equation. In this case, we can solve such equation by means of integrating factor method. The most important such equation has the form dy dx (3) where n € R, called the Bernoulli's equation or Bernoulli DE. If n = 0 or n = 1, then (3) is linear. Method of Solution: For n #1 If we multiply both sides of (3) by y", it becomes Let uy-n. Then = + R(x)y = S(x)y" du (1-n)y". da Multiply both sides of (4) by (1-n). = - dy dx 1-n +y¹-"R(x) = S(x) dy dx dy (1-n)y " +(1-n)y¹ R(x) = (1-n)S(x) dx The Bernoulli differential equation is now transformed into the form du +(1-n)R(x) u = (1-n)S(x) dx The above equation is now linear in u and can be solved by integrating factor method. du (6) d.x + P(x) u = f(x)
4. 2. dx + y² = xy (Bernoulli DE)
Transcribed Image Text:4. 2. dx + y² = xy (Bernoulli DE)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS