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In Problems 1 through 12, verify by substitution that each given function is a solution of the given differential equation. Throughout these problems, primes denote derivatives with re- spect to x. 1. y' = 3x2; y = x³ + 7 2. y' + 2y = 0; y = 3e-2x 3. y" + 4y = 0; yı = cos 2x, y2 = sin 2.x 4. y" = 9y; yı = e3x, y2 = e-3x 5. y' = y + 2e-x; y = e* – e=x 6. y" + 4y' + 4y = 0; y1 = e-2x, y2 = xe-2x 7. y" – 2y' + 2y = 0; y1 = e* cos x, y2 = e* sin x 8. y"+ y = 3 cos 2.x, yı = cos x – cos 2.x, y2 = sin x – cos 2x 9. y' + 2xy² = 0; y = T+ x² 10. х2у" + ху'—у 3D In x; y1 — х —In x, y2 In x In x 11. x²y" + 5xy' + 4y = 0; y1 = - V2 = х2 12. x2y" – xy' + 2y = 0; y1 = x cos(In x), y2 = x sin(In x)

In Problems 1 through 12, verify by substitution that each given function is a solution of the given differential equation. Throughout these problems, primes denote derivatives with re- spect to x. 1. y' = 3x2; y = x³ + 7 2. y' + 2y = 0; y = 3e-2x 3. y" + 4y = 0; yı = cos 2x, y2 = sin 2.x 4. y" = 9y; yı = e3x, y2 = e-3x 5. y' = y + 2e-x; y = e* – e=x 6. y" + 4y' + 4y = 0; y1 = e-2x, y2 = xe-2x 7. y" – 2y' + 2y = 0; y1 = e* cos x, y2 = e* sin x 8. y"+ y = 3 cos 2.x, yı = cos x – cos 2.x, y2 = sin x – cos 2x 9. y' + 2xy² = 0; y = T+ x² 10. х2у" + ху'—у 3D In x; y1 — х —In x, y2 In x In x 11. x²y" + 5xy' + 4y = 0; y1 = - V2 = х2 12. x2y" – xy' + 2y = 0; y1 = x cos(In x), y2 = x sin(In x)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 25CR
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In Problems 1 through 12, verify by substitution that each given function is a solution of the given differential equation. Throughout these problems, primes denote derivatives with re- spect to x. 1. y' = 3x2; y = x³ + 7 2. y' + 2y = 0; y = 3e-2x 3. y" + 4y = 0; yı = cos 2x, y2 = sin 2.x 4. y" = 9y; yı = e3x, y2 = e-3x 5. y' = y + 2e-x; y = e* – e=x 6. y" + 4y' + 4y = 0; y1 = e-2x, y2 = xe-2x 7. y" – 2y' + 2y = 0; y1 = e* cos x, y2 = e* sin x 8. y"+ y = 3 cos 2.x, yı = cos x – cos 2.x, y2 = sin x – cos 2x 9. y' + 2xy² = 0; y = T+ x² 10. х2у" + ху'—у 3D In x; y1 — х —In x, y2 In x In x 11. x²y" + 5xy' + 4y = 0; y1 = - V2 = х2 12. x2y" – xy' + 2y = 0; y1 = x cos(In x), y2 = x sin(In x)
Transcribed Image Text:In Problems 1 through 12, verify by substitution that each given function is a solution of the given differential equation. Throughout these problems, primes denote derivatives with re- spect to x. 1. y' = 3x2; y = x³ + 7 2. y' + 2y = 0; y = 3e-2x 3. y" + 4y = 0; yı = cos 2x, y2 = sin 2.x 4. y" = 9y; yı = e3x, y2 = e-3x 5. y' = y + 2e-x; y = e* – e=x 6. y" + 4y' + 4y = 0; y1 = e-2x, y2 = xe-2x 7. y" – 2y' + 2y = 0; y1 = e* cos x, y2 = e* sin x 8. y"+ y = 3 cos 2.x, yı = cos x – cos 2.x, y2 = sin x – cos 2x 9. y' + 2xy² = 0; y = T+ x² 10. х2у" + ху'—у 3D In x; y1 — х —In x, y2 In x In x 11. x²y" + 5xy' + 4y = 0; y1 = - V2 = х2 12. x2y" – xy' + 2y = 0; y1 = x cos(In x), y2 = x sin(In x)
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