Explanation Method used: Separation of variables: “Suppose we are given a first-order separable differential equation in the form, d y d x = f ( x ) g ( y ) Step 1: Separate the variables by writing d y d x = f ( x ) g ( y ) in the form, d y g ( y ) = f ( x ) d x Step 2: Integrate each side of d y g ( y ) = f ( x ) d x with respect to the appropriate variable”. Calculation: The given differential equation is d y d x = 2 x e − y . Step 1: Separate the variables as mentioned in above step 1. e y d y = 2 x d x Step 2: Integrate the above equation with respect to the appropriate variable as follows. ∫ e y d y = 2 ∫ x d x e y = 2 [ x 1 + 1

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage 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 9.2, Problem 26E

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The solution of first-order differential equation y′=2xe−y for the initial condition of y(0)=1.

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Chapter 9.2, Problem 25E

Chapter 9.2, Problem 27E

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Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

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The solution of first-order differential equation y ′ = 2 x e − y for the initial condition of y ( 0 ) = 1 .

Solution Summary: The author explains the solution of the first-order differential equation yprime = 2xe-y.

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