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Find the particular solution. yey(0) = 6 Step 1 Since the first-order differential equation is of the form = f(x), and f(x) is a continuous function, we can find the solution to the equation using integration. That is, y = fex-%dx. Recall the Exponential Formula for integrals given by eu' dx = e" + C. In this case, u = x - 9 and u' = 1. Use this substitution to find y as a function of x. ·1· 1dx y = -u' dx + C +6−1 / + C+c²-9| Step 2 Integration has given us the general solution y + C. A particular solution meets the condition y(0) = 6, which allows us to determine the constant C in the general solution. +c=6 C-6- That's it! Substituting 0 for x in the general solution gives y(0) = Because y(0) = 6 as well, e9+C = 6. Solve for C. +C - + C. Substitute the value for the constant C into the general solution. y=e* Finally, give a full equation for the particular solution to the differential equation when y(0) = 6.

Find the particular solution. yey(0) = 6 Step 1 Since the first-order differential equation is of the form = f(x), and f(x) is a continuous function, we can find the solution to the equation using integration. That is, y = fex-%dx. Recall the Exponential Formula for integrals given by eu' dx = e" + C. In this case, u = x - 9 and u' = 1. Use this substitution to find y as a function of x. ·1· 1dx y = -u' dx + C +6−1 / + C+c²-9| Step 2 Integration has given us the general solution y + C. A particular solution meets the condition y(0) = 6, which allows us to determine the constant C in the general solution. +c=6 C-6- That's it! Substituting 0 for x in the general solution gives y(0) = Because y(0) = 6 as well, e9+C = 6. Solve for C. +C - + C. Substitute the value for the constant C into the general solution. y=e* Finally, give a full equation for the particular solution to the differential equation when y(0) = 6.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the particular solution. y'=e*; y(0) = 6 Step 1 Since the first-order differential equation is of the form y = Sex 'dx. Recall the Exponential Formula for integrals given by e'u' dx = e" + C. In this case, u = x-9 and u' = 1. Use this substitution to find y as a function of x. y = [= - 1dx e²-u' dx +6- C+c²-9 = f(x), and f(x) is a continuous function, we can find the solution to the equation using integration. That is, That's it! Step 2 Integration has given us the general solution y = -9 + C. A particular solution meets the condition y(0) = 6, which allows us to determine the constant C in the general solution. Substituting 0 for x in the general solution gives y(0) = eº 9 + C. + C = 6. Solve for C. Because y(0) = 6 as well, +C = 6 +C = 6 C = 6- Substitute the value for the constant C into the general solution. y = ex-9 + C y = ex-9+ Finally, give a full equation for the particular solution to the differential equation when y(0) = 6.
Transcribed Image Text:Find the particular solution. y'=e*; y(0) = 6 Step 1 Since the first-order differential equation is of the form y = Sex 'dx. Recall the Exponential Formula for integrals given by e'u' dx = e" + C. In this case, u = x-9 and u' = 1. Use this substitution to find y as a function of x. y = [= - 1dx e²-u' dx +6- C+c²-9 = f(x), and f(x) is a continuous function, we can find the solution to the equation using integration. That is, That's it! Step 2 Integration has given us the general solution y = -9 + C. A particular solution meets the condition y(0) = 6, which allows us to determine the constant C in the general solution. Substituting 0 for x in the general solution gives y(0) = eº 9 + C. + C = 6. Solve for C. Because y(0) = 6 as well, +C = 6 +C = 6 C = 6- Substitute the value for the constant C into the general solution. y = ex-9 + C y = ex-9+ Finally, give a full equation for the particular solution to the differential equation when y(0) = 6.
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