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dt erencial aquation is separable, in other words, we can write it in the form = p(t) q(y). What are the two functions p(t) and g(y)? (t) - - 3 low separate Lhe variables. Integrate both sides of the resulting equation with respect to t and replace dy dt by dy in the integral on the left side, 4y dy = - 3 dt Do the integratlons on both sides. Use k to stand for your constant of integration for left side and K to stand for your constant of integration for the right side. (Lower case k on leſl side, upper case K on right side.) -4y Entegrating left side gives: +k Integrating right side gives: -3t + K We can combine the two constants of integration Into a single consturit, C, that appears as +C on the right side of our eguatiori. (We do this by subtracting k trom both sides of the equation.) Write the new constant C in terms ofk and K K-k

dt erencial aquation is separable, in other words, we can write it in the form = p(t) q(y). What are the two functions p(t) and g(y)? (t) - - 3 low separate Lhe variables. Integrate both sides of the resulting equation with respect to t and replace dy dt by dy in the integral on the left side, 4y dy = - 3 dt Do the integratlons on both sides. Use k to stand for your constant of integration for left side and K to stand for your constant of integration for the right side. (Lower case k on leſl side, upper case K on right side.) -4y Entegrating left side gives: +k Integrating right side gives: -3t + K We can combine the two constants of integration Into a single consturit, C, that appears as +C on the right side of our eguatiori. (We do this by subtracting k trom both sides of the equation.) Write the new constant C in terms ofk and K K-k

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 43E
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All answers provide are correct just need help on last question
In this question, you will solve the differential equalion ay = e4ytA - 3ey. This differential equation is separable, in other words, we can write it in the form * = p(t) aly). dt What are the two functions p(t) and g(y)? P(t) =4 q(y) =t Now separate the variables. Integrate both sides of the resulting equation with respect to t and replace Ydt by dy in the integral on the left side. dt" dy = 4y A- 3 dt Do the integratlons on both sides. Use k to stand for your constant of integration for the left side and K to stand for your constant of integration for the right side. (Lowar case k on left side, upper case K on right side.) 1 -4y Integrating left side gives: Te +k Integrating right side gives: - 3t + K We can combine the two constants of integration Into a single consturil, C, that appears as +C on the right side of our eguatiori. (We do this by subtracting k trom both sides of the equation.) Write the new constant C in terms ofk and K C= K-k
Transcribed Image Text:In this question, you will solve the differential equalion ay = e4ytA - 3ey. This differential equation is separable, in other words, we can write it in the form * = p(t) aly). dt What are the two functions p(t) and g(y)? P(t) =4 q(y) =t Now separate the variables. Integrate both sides of the resulting equation with respect to t and replace Ydt by dy in the integral on the left side. dt" dy = 4y A- 3 dt Do the integratlons on both sides. Use k to stand for your constant of integration for the left side and K to stand for your constant of integration for the right side. (Lowar case k on left side, upper case K on right side.) 1 -4y Integrating left side gives: Te +k Integrating right side gives: - 3t + K We can combine the two constants of integration Into a single consturil, C, that appears as +C on the right side of our eguatiori. (We do this by subtracting k trom both sides of the equation.) Write the new constant C in terms ofk and K C= K-k
Th MA 231 hy Tn MA 231 hy x 1 MA 231 hy x W MA 231, se WA Lesson 5, A X WA Lesson 7, B W. Lesson /, A A Lesson 5, B X +- i webassign.net/web/Student/Assignment-Responses/last?dep=27285613 Write the new constant C in terms of k and K C - K-k Note: For the rcst of this problem and for all problems following in this assignment, whenever we do separation of variables, we will use a single constant of integration, adding C to the right side. Even if it is possible to simplify (like, for instance, when we wrote A= eC in an example in class), you should leave your answer in terms of C. Finally, rearrange to get y as a function of t. (The constant of integration, C, will appear in your answer.)
Transcribed Image Text:Th MA 231 hy Tn MA 231 hy x 1 MA 231 hy x W MA 231, se WA Lesson 5, A X WA Lesson 7, B W. Lesson /, A A Lesson 5, B X +- i webassign.net/web/Student/Assignment-Responses/last?dep=27285613 Write the new constant C in terms of k and K C - K-k Note: For the rcst of this problem and for all problems following in this assignment, whenever we do separation of variables, we will use a single constant of integration, adding C to the right side. Even if it is possible to simplify (like, for instance, when we wrote A= eC in an example in class), you should leave your answer in terms of C. Finally, rearrange to get y as a function of t. (The constant of integration, C, will appear in your answer.)
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