Explanation Definition used: For first order linear differential equation of the form y ' ( x ) + P ( x ) y = Q ( x ) . And the solution will be of the form y ( x ) = ∫ e ∫ P ( x ) d x Q ( x ) d x + C e ∫ P ( x ) d x . Calculation: Consider the given differential equation is y ′ ( t ) = y − t . To solve first order linear differential equation P ( t ) = − 1 , Q ( t ) = − t , y ( t ) = ∫ e − ∫ d t ( − t ) d t + C e − ∫ d t y ( t ) = ∫ e − t ( − t ) d t + C e − t

2nd Edition

ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

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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 7, Problem 100RE

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To sketch: The direction field for the differential equation y′(t)=y−t and the solution curve corresponds to the initial condition y(−2)=12.

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Chapter 7, Problem 99RE

Chapter 7, Problem 101RE

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The direction field for the differential equation y ′ ( t ) = y − t and the solution curve corresponds to the initial condition y ( − 2 ) = 1 2 .

Solution Summary: The author illustrates the direction field for the differential equation yprime(t)=y-t and the solution curve corresponds to the initial condition.

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To sketch: The direction field for the differential equation y′(t)=y−t and the solution curve corresponds to the initial condition y(−2)=12.

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