Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
A function f(x, y, z) is called homogeneous of degree > if f(bx, by, bz) = b^f(x, y, z) for b, A E R. Such functions are also called scale free. Prove Euler's theorem for homogeneous functions which states that if f(x, y, z) is homogeneous of degree X, then af af af I

A function f(x, y, z) is called homogeneous of degree > if f(bx, by, bz) = b^f(x, y, z) for b, A E R. Such functions are also called scale free. Prove Euler's theorem for homogeneous functions which states that if f(x, y, z) is homogeneous of degree X, then af af af I

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

Hello,

Can someone please show how to solve this problem?

Thank you!

Problem 6.5 OPTIONAL PROBLEM - Homogeneous functions A function f(x, y, z) is called homogeneous of degree > if f(bx, by, bz) = b^f(x, y, z) for b, A E R. Such functions are also called scale free. Prove Euler's theorem for homogeneous functions which states that if f(x, y, z) is homogeneous of degree X, then af af af x +y +z = əx dy Əz Xf. Hint: Define intermediate variables u = bx, v= by and w bz. Then, differentiate the given equation f(bx, by, bz) = bf(x, y, z) with respect to x, y, z and b, using the chain rule.
Transcribed Image Text:Problem 6.5 OPTIONAL PROBLEM - Homogeneous functions A function f(x, y, z) is called homogeneous of degree > if f(bx, by, bz) = b^f(x, y, z) for b, A E R. Such functions are also called scale free. Prove Euler's theorem for homogeneous functions which states that if f(x, y, z) is homogeneous of degree X, then af af af x +y +z = əx dy Əz Xf. Hint: Define intermediate variables u = bx, v= by and w bz. Then, differentiate the given equation f(bx, by, bz) = bf(x, y, z) with respect to x, y, z and b, using the chain rule.
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