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# Constant Multiples of Solutions.(a) Show that y = e-x is a ISBN: 9780321747730 43

## Solution for problem 28E Chapter 2.3

Fundamentals of Differential Equations | 8th Edition

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Problem 28E

Constant Multiples of Solutions.(a) Show that y = e-x is a solution of the linear equation And y = x-1 is a solution of the nonlinear equation (b) Show that for any constant C, the function Ce-x is a solution of equation (16), while Cx-1 is a solution of equation (17) only when C = 0 or 1.(c) Show that for any linear equation of the form if y (x) is a solution, then for any constant C the function Cy(x)is also a solution.

Step-by-Step Solution:

SolutionStep 1In this problem, we have to show that is a solution of the homogenous equation And is a solution of the nonlinear equation. b)In the next part, we have to show that for any constant C, the function Ce-x is a solution of equation , while Cx-1 is a solution of equation only when C = 0 or 1.c)In this problem we have to show that for any linear equation of the form if (x) is a solution, then for any constant C the function C(x)is also a solution.Step 2Method of Solving linear equationFirst we have to write the equation in standard form Compare the standard form with the giving equation So, we have Now, we have to calculate the integrating factor Then, Now, we have to multiply the standard equation with or = Hence, we can say that is a solution of the homogenous equationStep 3Method of Solving linear equationFirst we have to write the equation in standard form Compare the standard form with the giving equation...

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##### ISBN: 9780321747730

Since the solution to 28E from 2.3 chapter was answered, more than 298 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 28E from chapter: 2.3 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. The answer to “Constant Multiples of Solutions.(a) Show that y = e-x is a solution of the linear equation And y = x-1 is a solution of the nonlinear equation (b) Show that for any constant C, the function Ce-x is a solution of equation (16), while Cx-1 is a solution of equation (17) only when C = 0 or 1.(c) Show that for any linear equation of the form if y (x) is a solution, then for any constant C the function Cy(x)is also a solution.” is broken down into a number of easy to follow steps, and 84 words. This full solution covers the following key subjects: solution, equation, any, constant, show. This expansive textbook survival guide covers 67 chapters, and 2118 solutions. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8.

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