A Bernoulli differential equation is one of the form dy/dx + P(x)y =Q(x)y^n. Observe that, if n=0 or 1 , the Bernoulli equation is linear. For other values of n , the substitution u=y^(1−n) transforms the Bernoulli equation into the linear equation (du/dx) + (1-n)P(x)u=(1-n)Q(x). Use an appropriate substitution to solve the equation xy'+y=6xy^2,

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

A Bernoulli differential equation is one of the form

dy/dx + P(x)y =Q(x)y^n.

Observe that, if n=0 or 1 , the Bernoulli equation is linear.

For other values of n , the substitution u=y^(1−n) transforms the Bernoulli equation into the linear equation

(du/dx) + (1-n)P(x)u=(1-n)Q(x).

Use an appropriate substitution to solve the equation

xy'+y=6xy^2,

and find the solution that satisfies y(1)=8.

Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

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,