Consider the equation dy dx = y - 4x x-y which is not separable. (a). Show that the above equation can be rewritten as dy = (y/x) - 4 dx 1 – (y/x) • - (b). Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x, v, and dv/dx. (c). Replace y and dy/dx in the equation part (a) by the expressions from part (b) that involve v and do/dx. Show that the resulting differential equation of v is separable, and solve it. (d). Find the solution y(x) by replacing o by y/x in the solution in part (c).
Consider the equation dy dx = y - 4x x-y which is not separable. (a). Show that the above equation can be rewritten as dy = (y/x) - 4 dx 1 – (y/x) • - (b). Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x, v, and dv/dx. (c). Replace y and dy/dx in the equation part (a) by the expressions from part (b) that involve v and do/dx. Show that the resulting differential equation of v is separable, and solve it. (d). Find the solution y(x) by replacing o by y/x in the solution in part (c).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Related questions
Question
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 1 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University