Explanation Given: The first order differential equation is ( y − x ) y ′ = y − x + 8 . Definition: “A solution in which the dependent variable is expressed solely in terms of the independent variable and constant is said to be an explicit solution.” Calculation: Consider the function y = x + 4 x + 2 . The function y is defined only when, x + 2 ≥ 0 x ≥ − 2 As y ′ is not defined at x = − 2 . Thus, the domain of the function is ( − 2 , ∞ ) . Consider the given differential equation y = x + 4 x + 2 and the given function ( y − x ) y ′ = y − x + 8 . From the derivative, d d x ( y ) = d d x ( x + 4 x + 2 ) y ′ = d d x ( x ) + 4 d d x ( x + 2 ) = 1 + 4 2 ( x + 2 ) d d x ( x + 2 ) = 1 + 2 ( x + 2 ) The given function becomes, (

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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 1.1, Problem 15E

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To verify: The function y=x+4x+2 is a solution of the given first order differential equation.

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Chapter 1.1, Problem 14E

Chapter 1.1, Problem 16E

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To verify: The function y = x + 4 x + 2 is a solution of the given first order differential equation.

Solution Summary: The author explains that the function y=x+4sqrtx +2 is a solution of the first order differential equation.

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To verify: The function y=x+4x+2 is a solution of the given first order differential equation.

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