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Homework No. (3) Higher Order Differential Equations Math 203: ODES In each of problems 1–12 Solve the given differential equations and the given IVPS. 1. y (w) +y"'=x 2. 16y ) – 8y"+y =0 3. у )— Зу о) + 3у" - у" %3D0 (iv) 4. у -4y" =x? +e* 5. y"'+2y"-5y'-6y =100e-* +18e¬* 6. y"' – 3y"+ 3y'- y =-3sin 5x 7. y"+y'=-2 sin 2x 8. у"" + Зу" + 3y'+ у %3D30 cosx 9. 4y " +8y"+41y'+37y = 0, y (0)= 9, y'(0)=-6.5, y"(0)=-39.75 (iv) 10. у ) - 16у %3D128 сosh 2x, y (0) %3D1, у"(0) — 24, у" (0)-20, у " (0) —-160 (iv 11. у +6y " +17y"+22y'+14y = 0, y (0) =1, y'(0) =-2, y"(0) = 0, y"'(0)=3 (iv ) 12. у + 2y " + y" +8y' –12y =12sin.x -e*, y (0)= 3, y'(0)=0, y"(0)=-1, y''(0)=2 In each of problems 13–14 Determine whether the given set of functions in linearly independent or linearly dependent. 13. f, (x ) =x' +1, f;(x)=x² +x +1, ƒ;(x ) = 2x² - 2 14. fi (x ) =e*, f2(x)=e* , f;(x ) =1 In each of problems 15–17 Solve the given Euler-Cauchy equations. 15. x 'y " + 7x ?y "-2xy'-10y = 0, y (1)=1, y'(1)=-7, y "(1) = 44 16. х у " -x²y"- 2xy'+2y = 2x * 17. х Ву " +х*у"- бху'+6у — 4х* r 2 In each of problems 17–18 Using the method of Variation of Parameters to solve the following equation. 18. у - y'=x 19. х *у " +х?у" - 2ху'+2у %3D2x 4 x'y 20. Solve the non-linear equation 2x *(y ")'y"' + 4x ³ (y")' = y".

Homework No. (3) Higher Order Differential Equations Math 203: ODES In each of problems 1–12 Solve the given differential equations and the given IVPS. 1. y (w) +y"'=x 2. 16y ) – 8y"+y =0 3. у )— Зу о) + 3у" - у" %3D0 (iv) 4. у -4y" =x? +e* 5. y"'+2y"-5y'-6y =100e-* +18e¬* 6. y"' – 3y"+ 3y'- y =-3sin 5x 7. y"+y'=-2 sin 2x 8. у"" + Зу" + 3y'+ у %3D30 cosx 9. 4y " +8y"+41y'+37y = 0, y (0)= 9, y'(0)=-6.5, y"(0)=-39.75 (iv) 10. у ) - 16у %3D128 сosh 2x, y (0) %3D1, у"(0) — 24, у" (0)-20, у " (0) —-160 (iv 11. у +6y " +17y"+22y'+14y = 0, y (0) =1, y'(0) =-2, y"(0) = 0, y"'(0)=3 (iv ) 12. у + 2y " + y" +8y' –12y =12sin.x -e*, y (0)= 3, y'(0)=0, y"(0)=-1, y''(0)=2 In each of problems 13–14 Determine whether the given set of functions in linearly independent or linearly dependent. 13. f, (x ) =x' +1, f;(x)=x² +x +1, ƒ;(x ) = 2x² - 2 14. fi (x ) =e*, f2(x)=e* , f;(x ) =1 In each of problems 15–17 Solve the given Euler-Cauchy equations. 15. x 'y " + 7x ?y "-2xy'-10y = 0, y (1)=1, y'(1)=-7, y "(1) = 44 16. х у " -x²y"- 2xy'+2y = 2x * 17. х Ву " +х*у"- бху'+6у — 4х* r 2 In each of problems 17–18 Using the method of Variation of Parameters to solve the following equation. 18. у - y'=x 19. х *у " +х?у" - 2ху'+2у %3D2x 4 x'y 20. Solve the non-linear equation 2x *(y ")'y"' + 4x ³ (y")' = y".

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Homework No. (3) Higher Order Differential Equations Math 203: ODES In each of problems 1–12 Solve the given differential equations and the given IVPS. 1. y (*) + y'' = x 2. 16y *) –8y"+y = 0 3. y")– 3y (*) + 3y"' – y" = 0 (v) 4. у - 4y +e* 5. у " +2у"-5у'-6у %3D100е-3* +18e * 6. y " – 3y"+ 3y'– y =-3sin 5x 7. y"'+y'= -2 sin 2x 8. y" +3y"+3y'+y =30cos.x 9. 4y " +8y"+41y'+37y = 0, y (0)= 9, y'(0)=-6.5, y"(0): = -39.75 10. y") – 16y =128 cosh 2x , y (0) =1, y'(0)= 24, y"(0)= 20, y"'(0)=-160 11. y(*) +6y "+17y"+22y'+14y = 0, y (0) =1, y'(0)=-2, y"(0)=0, y''(0)=3 12. y (*) + 2y "'+ y" +8y'-12y =12sin.x e*, y (0)=3, y'(0)=0, y"(0) =-1, y"'(0)= 2 In each of problems 13–14 Determine whether the given set of functions in linearly independent or linearly dependent. 13. f, (x )= x' +1, f; (x ) 14. f. (x ) =e*, f2(x)=e*,f;(x )=1 )=x² +x +1, f3(x )= 2x² – 2 In each of problems 15–17 Solve the given Euler-Cauchy equations. 15. х *у -7x 'у"- 2ху'-10у 3 0, у (1)-1, у'(1) --7, у "(1) -44 16. х °у 3, " +x?y"- 2xy'+2y =2x * 17. х *у " +x у"- бху'+6у %3D4x? In each of problems 17–18 Using the method of Variation of Parameters to solve the following equation. 18. у - y'=x 19. х *у +x*y"- 2ху' +2у %3D 2х 20. Solve the non-linear equation 2x * (y ")°y "' + 4x ³ (y")' = y".
Transcribed Image Text:Homework No. (3) Higher Order Differential Equations Math 203: ODES In each of problems 1–12 Solve the given differential equations and the given IVPS. 1. y (*) + y'' = x 2. 16y *) –8y"+y = 0 3. y")– 3y (*) + 3y"' – y" = 0 (v) 4. у - 4y +e* 5. у " +2у"-5у'-6у %3D100е-3* +18e * 6. y " – 3y"+ 3y'– y =-3sin 5x 7. y"'+y'= -2 sin 2x 8. y" +3y"+3y'+y =30cos.x 9. 4y " +8y"+41y'+37y = 0, y (0)= 9, y'(0)=-6.5, y"(0): = -39.75 10. y") – 16y =128 cosh 2x , y (0) =1, y'(0)= 24, y"(0)= 20, y"'(0)=-160 11. y(*) +6y "+17y"+22y'+14y = 0, y (0) =1, y'(0)=-2, y"(0)=0, y''(0)=3 12. y (*) + 2y "'+ y" +8y'-12y =12sin.x e*, y (0)=3, y'(0)=0, y"(0) =-1, y"'(0)= 2 In each of problems 13–14 Determine whether the given set of functions in linearly independent or linearly dependent. 13. f, (x )= x' +1, f; (x ) 14. f. (x ) =e*, f2(x)=e*,f;(x )=1 )=x² +x +1, f3(x )= 2x² – 2 In each of problems 15–17 Solve the given Euler-Cauchy equations. 15. х *у -7x 'у"- 2ху'-10у 3 0, у (1)-1, у'(1) --7, у "(1) -44 16. х °у 3, " +x?y"- 2xy'+2y =2x * 17. х *у " +x у"- бху'+6у %3D4x? In each of problems 17–18 Using the method of Variation of Parameters to solve the following equation. 18. у - y'=x 19. х *у +x*y"- 2ху' +2у %3D 2х 20. Solve the non-linear equation 2x * (y ")°y "' + 4x ³ (y")' = y".
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