Explanation Procedure used: General solution of differential equation using method of reduction of order: 1. Consider the DE and substitute, u = y ′ into the DE. 2. Use separation of variable to reduce the order. 3. Substitute, the boundary values to find the constants. 4. Substitute, the constants in final solution. Calculation: Consider the DE y ′ y ″ = 4 x . Substitute u = y ′ into y ′ y ″ = 4 x , u ( u ′ ) = 4 x u d u d x = 4 x Use the variable separation method to separate the variables and then integrate. ∫ u d u = ∫ 4 x d x u 2 2 = 4 x 2 2 u 2 2 = 2 x 2 + c 1 1 2 ( y ′ ) 2 = 2 x 2 + c 1 ( ∵ u = y ′ ) Substitute x = 1 and y ′ ( 1 ) = 2 in the above equation

Differential Equations with Boundary-Value Problems (MindTap Course List)

9th Edition

ISBN: 9781305965799

Author: Dennis G. Zill

Publisher: Cengage Learning

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Chapter 4, Problem 43RE

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To solve: The differential equation y′y″=4x with the boundary values y(1)=5 and y′(1)=2.

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Chapter 4, Problem 42RE

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Differential Equations with Boundary-Value Problems (MindTap Course List)

Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - Given that y=c1+c2x2 is a two-parameter family of...Ch. 4.1 - Find two members of the family of solutions in...Ch. 4.1 - Prob. 7E Ch. 4.1 - Use the general solution of x + 2x = 0 given in...Ch. 4.1 - In Problems 9 and 10 find an interval centered...Ch. 4.1 - In Problems 9 and 10 find an interval centered...

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The differential equation y ′ y ″ = 4 x with the boundary values y ( 1 ) = 5 and y ′ ( 1 ) = 2 .

Solution Summary: The author explains how to solve the differential equation using the method of reduction of order.

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To solve: The differential equation y′y″=4x with the boundary values y(1)=5 and y′(1)=2.

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