Use the method discussed under “Homogeneous Equations” to solve 9–16.
Step 1 of 3
Solution:Step-1:In this problem we need to solve the homogeneous differential equation .Step-2:Given equation is :.Homogeneous equation definition: If the right hand side of the equation can be expressed as a function of the ratio alone , then we say the equation is homogeneous.Now the given equation can be expressed as, ……..(1)Therefore, the given equation is a homogeneous equation.Step-3:Substitute y = vx , then differentiate on both sides with respect to x we get:, since and ………..(2)From (1) and (2) we get. .Now it is in variable separable formStep-4:Integrating on both sides we get.Multiply both sides with 3 we get., since , where c is any constant. , since ln(a/b) = ln(a)-ln(b). , where is any constant .step-5:Therefore, the solution of the differential equation is .
Textbook: Fundamentals of Differential Equations
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. This full solution covers the following key subjects: discussed, equations, homogeneous, method, under. This expansive textbook survival guide covers 67 chapters, and 2118 solutions. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Since the solution to 12E from 2.6 chapter was answered, more than 291 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 12E from chapter: 2.6 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. The answer to “Use the method discussed under “Homogeneous Equations” to solve 9–16.” is broken down into a number of easy to follow steps, and 10 words.