Explanation Given: The function y = x − 2 x is a solution of the DE x y ′ + y = 2 x . Procedure used: Solution to a differential equation: The n th-order ordinary differential equation is one dependent variable by the general form, F ( x , y , y ' , ... , y ( n ) ) = 0 Where F is a real valued function of n + 2 variables: x , y , y ' , ... , y ( n ) . The solution of an n th-order ordinary differential equation is a function ϕ that possesses at least n derivatives and satisfying the differential equation on interval I , i.e. F ( x , ϕ ( x ) , ϕ ' ( x ) , ... , ϕ ( n ) ( x ) ) = 0 for all x in I . Calculation: Consider the given differential equation x y ′ + y = 2 x and the given solution function y = x − 2 x . Observe that x = 0 is not a solution for the given differential equation

Differential Equations with Boundary-Value Problems

9th Edition

ISBN: 9781337632515

Author: Dennis G. Zill

Publisher: Cengage Learning US

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Chapter 1, Problem 19RE

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The value of x0 and the largest interval I for which y(x) is a solution of the first-order IVP xy′+y=2x,y(x0)=1.

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Chapter 1, Problem 18RE

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Differential Equations with Boundary-Value Problems

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The value of x 0 and the largest interval I for which y ( x ) is a solution of the first-order IVP x y ′ + y = 2 x , y ( x 0 ) = 1 .

Solution Summary: The author explains the function y=x-2x is a solution of the first-order IVP.

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The value of x0 and the largest interval I for which y(x) is a solution of the first-order IVP xy′+y=2x,y(x0)=1.

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