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+(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation. Problems In each of Problems 1 through 10, find the general solution of the given 15. + 2y differential equation. In each of Proble Xy" - 2y' - 3y = 3e²¹ Determ 2. y" - y' - 2y = -2t+4t² undetermin N b. Use of the giver 4. 3. y"+y'-6y = 12e³t+ 12e-2t y"-2y' - 3y = -3te-t y" +2y' = 3 + 4 sin(2t) 6. y" + 2y' + y = 2e-¹ ✓ "! I 3 in (2011 (24) 16. 17. y"-5y' - H 18. y" +2y' - y" + 3y': H

+(Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation. Problems In each of Problems 1 through 10, find the general solution of the given 15. + 2y differential equation. In each of Proble Xy" - 2y' - 3y = 3e²¹ Determ 2. y" - y' - 2y = -2t+4t² undetermin N b. Use of the giver 4. 3. y"+y'-6y = 12e³t+ 12e-2t y"-2y' - 3y = -3te-t y" +2y' = 3 + 4 sin(2t) 6. y" + 2y' + y = 2e-¹ ✓ "! I 3 in (2011 (24) 16. 17. y"-5y' - H 18. y" +2y' - y" + 3y': H

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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by 1. be If the nonhomogeneous function involves both cos(3t) and sin(ßt), it convenient to treat these terms together, since each one individually may give rise form for a particular solution. For example, if g(t) = t sint+2 cost, the form for Y(t) = (Aot + A₁) sint + (Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation. Xy" - 2y' - 3y = 3e²t 2. y" - y' - 2y = -2t+4t² Problems In each of Problems 1 through 10, find the general solution of the given 3. 4. 5. 6. y" +2y' + y = 2e¹ بود y"+y' - 6y = 12e³t + 12e-2t En 97 y"-2y' - 3y = -3te-t y" + 2y' = 3 + 4 sin(2t) 7. y"+y = 3 sin(2t) + t cos(2t) nogo 200 8. u" + wu = cos(wt), w² #wo 9. 3. u" + w₁u = cos(wot) ials by t to increase th (20) 15. y" +2y + al solution of In each of Proble Determ undetermin N b. Use a of the given 10. y” +y+4y = 2 sinh t Hint; sinh t =(e – e-)/2 In each of Problems 11 through 15, find the solution of the given initial value problem. 11. y"+y' - 2y = 2t, y(0) = 0, y'(0) = 1 12. y" + 4y = 1² +3e¹, y(0) = 0, y'(0) = 2 13. y" - 2y + y = te' +4, y(0) = 1, y'(0) = 1 14. y" +4y= 3 sin(2t), y(0) = 2, y'(0) = -1 16. y" + 3y' = 17. y" - 5y + 18. y" +2y + 19. y" + 4y = 20. y" +3y' + y" +2y + 21. 22. Consider th from Example 5 solutions of the c method of reduc nonhomogeneous where v (t) is to b
Transcribed Image Text:by 1. be If the nonhomogeneous function involves both cos(3t) and sin(ßt), it convenient to treat these terms together, since each one individually may give rise form for a particular solution. For example, if g(t) = t sint+2 cost, the form for Y(t) = (Aot + A₁) sint + (Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation. Xy" - 2y' - 3y = 3e²t 2. y" - y' - 2y = -2t+4t² Problems In each of Problems 1 through 10, find the general solution of the given 3. 4. 5. 6. y" +2y' + y = 2e¹ بود y"+y' - 6y = 12e³t + 12e-2t En 97 y"-2y' - 3y = -3te-t y" + 2y' = 3 + 4 sin(2t) 7. y"+y = 3 sin(2t) + t cos(2t) nogo 200 8. u" + wu = cos(wt), w² #wo 9. 3. u" + w₁u = cos(wot) ials by t to increase th (20) 15. y" +2y + al solution of In each of Proble Determ undetermin N b. Use a of the given 10. y” +y+4y = 2 sinh t Hint; sinh t =(e – e-)/2 In each of Problems 11 through 15, find the solution of the given initial value problem. 11. y"+y' - 2y = 2t, y(0) = 0, y'(0) = 1 12. y" + 4y = 1² +3e¹, y(0) = 0, y'(0) = 2 13. y" - 2y + y = te' +4, y(0) = 1, y'(0) = 1 14. y" +4y= 3 sin(2t), y(0) = 2, y'(0) = -1 16. y" + 3y' = 17. y" - 5y + 18. y" +2y + 19. y" + 4y = 20. y" +3y' + y" +2y + 21. 22. Consider th from Example 5 solutions of the c method of reduc nonhomogeneous where v (t) is to b
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