Explanation Formula used: A first-order differential equation of the form d y d x = g ( x ) h ( y ) is said to be separable or to have separable variables. Calculation: The given differential equation is x 2 y ″ + ( y ′ ) 2 = 0 . Let u = y ′ so that u ′ = y ″ . The given equation becomes x 2 u ′ + u 2 = 0 . Separate the variables to get x 2 u ′ = − u 2 d u d x x 2 = u 2 − u − 2 d u = x − 2 d x Take the integral of the above equation and simplify − ∫ u − 2 d u = ∫ x − 2 d x u − 1 = − x − 1 + c 1 u = 1 c 1 − x − 1 Since, u = y ′ , so y ′ = u = 1 c 1 − x − 1 Take the integral of the above equation

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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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 3.7, Problem 5E

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The solution of the given differential equation x2y″+(y′)2=0 by using the substitution u=y′.

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Chapter 3.7, Problem 4E

Chapter 3.7, Problem 6E

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The solution of the given differential equation x 2 y ″ + ( y ′ ) 2 = 0 by using the substitution u = y ′ .

Solution Summary: The author explains the solution of the first-order differential equation x2y′′+left, and the formula used to solve it.

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The solution of the given differential equation x2y″+(y′)2=0 by using the substitution u=y′.

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