In 1–8, classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.
SOLUTIONStep 1We have to check the given differential equation is separable, linear, exact.Step 2First we check given equation is linear or not.We have, a first order linear equation is of the form,Step 3Given differential equation is Which is not of the form Therefore it is not linear.Step 4Next we have to check it is separable or not.Step 5If the given differential equation is separable, then it can be written as f()d = g(y)dyStep 6.Given differential equation is This can not be expressed is of the form f()d = g(y)dy.Therefore this is not separable.Step 7Next we have to check the given differential equation is exact or not.We have, a differential equation M dx+N dy is exact if and only if Step 8Given equation is and Find = 2y= 2yHere Therefore the given differential equation is exact.Step 9We conclude that the given differential equation, is exact is not linear and is not separable.
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. Since the solution to 6E from 2.4 chapter was answered, more than 244 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 6E from chapter: 2.4 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. This full solution covers the following key subjects: Classification, classify, equation, equations, exact. This expansive textbook survival guide covers 67 chapters, and 2118 solutions. The answer to “In 1–8, classify the equation as separable, linear, exact, or none of these. Notice that some equations may have more than one classification.” is broken down into a number of easy to follow steps, and 23 words. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8.