According to Ince [pg. 531] the first known use of integrating factors to solve a differential equation was by Fatio de Duiller in June of 1687. He was solving the equation 3xdy2ydx = 0 which we would write in standard form (using the prime notation) as For this equation the integrating factor is: After multiplying both sides by the integrating factor and unapplying the product rule we get the new differential equation: del 94 ] = Integrating both sides we get the algebraic equation Solving for y, the solution to the differential equation is y = (using C as the constant)
According to Ince [pg. 531] the first known use of integrating factors to solve a differential equation was by Fatio de Duiller in June of 1687. He was solving the equation 3xdy2ydx = 0 which we would write in standard form (using the prime notation) as For this equation the integrating factor is: After multiplying both sides by the integrating factor and unapplying the product rule we get the new differential equation: del 94 ] = Integrating both sides we get the algebraic equation Solving for y, the solution to the differential equation is y = (using C as the constant)
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
![According to Ince [pg. 531] the first known use of integrating factors to solve a differential equation was by Fatio de Duiller in June of
1687. He was solving the equation
3xdy - 2ydx = 0
which we would write in standard form (using the prime notation) as
Integrating both sides we get the algebraic equation
Solving for y, the solution to the differential equation is y =
=
For this equation the integrating factor is:
After multiplying both sides by the integrating factor and unapplying the product rule we get the new differential equation:
da [
]
(using C as the constant)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3208712-9894-42ea-9704-5a16f12691ec%2Fd6a10019-4dd4-4b16-96b6-83b4ef1cb256%2Fye0gqa_processed.png&w=3840&q=75)
Transcribed Image Text:According to Ince [pg. 531] the first known use of integrating factors to solve a differential equation was by Fatio de Duiller in June of
1687. He was solving the equation
3xdy - 2ydx = 0
which we would write in standard form (using the prime notation) as
Integrating both sides we get the algebraic equation
Solving for y, the solution to the differential equation is y =
=
For this equation the integrating factor is:
After multiplying both sides by the integrating factor and unapplying the product rule we get the new differential equation:
da [
]
(using C as the constant)
Expert Solution
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 2 steps with 2 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,
