Explanation Given: Few differential equations and few solutions. d y d x = y x (i) y = x 3 d y d x = 3 y x (ii) y = 3 x d y d x = 3 x (iii) y = e 3 x d y d x = y (iv) y = 3 e x d y d x = 3 y (v) y = x Formula Used: The general solution to the differential equation d y d t = k y is given as y = C e k t , where C is any constant Calculation: Let consider the differential equation d y d x = y x Separate the variables. d y y = d x x Taking integral on both sides, we get ∫ d y y = ∫ d x x ln | y | = ln | x | y = x Thus, solution to differential equation d y d x = y x is y = x . Let consider the differential equation d y d x = 3 y x Separate the variables. d y y = 3 d x x Taking integral on both sides, we get ∫ d y y = ∫ 3 d x x ∫ d y y = 3 ∫ d x x ln | y | = 3 ln | x | ln | y | = ln | x 3 | y = x 3 Thus, solution to differential equation d y d x = 3 y x is y = x 3

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 9.2, Problem 22P

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Match solutions with the appropriate differential equation.

Solution Summary: The author explains that the general solution to the differential equation is given as y=Cekt.

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Match solutions with the appropriate differential equation.

Chapter 9 Solutions