In each of Problems 5 through 9, verify that each given function is a solution of the differential equation.5. ?′′ − ? = 0; ?(?) = ??6. ?′′ + 2?′ − 3? = 0; ?(?) = ?−3?7. ??′ − ? = ?2; ? = 3? + ?28. ?′′′′ + 4?′′′ + 3? = ?; ?(?) =?39. ?2?′′ + 5??′ + 4? = 0; ?(?) = ?−2 DITO VOLTE167ll *B/s0( (59 14, 3:29No service+ Activity 1.pdfActivity 1.A. In each of Problems 1 through 4, determine the order and the degree of the givendifferential equation; also state whether the equation is linear or nonlinear.1. t+ t+ 2y = sint2. (1+ v?)d'y+ y = etdt3. + ar+dt2d²y+ y = 1dtdt4.dtd²yz + sin(t + y) = sin tB. In each of Problems 5 through 9, verify that each given function is a solution of thedifferential equation.5. y" – y = 0; y(t) = et6. y" + 2y' – 3y = 0; y(t) = e-3t7. ty' – y = t2; y = 3t + t28. y" + 4y" + 3y = t; y(t) = =9. t'y" + 5ty' + 4y = 0; y(t) = t-2C. In each of Problems 10 through 11, determine the values of r for which the givendifferential equation has solutions of the form y = et.10. y" + y' – 6y = 011. y" – 3y" + 2y' = 0D. In each of Problems 12 through 15, eliminate the arbitrary constant using the metheyou're comfortable with.12. y = 3AX3 + 2BX² + 4Cx - D13. x?y³ + x³y5 = C14. y = -2C,e-3* + Cze*x15. y = C,e-3x – 2C2e-3*d for the exclusive use of SLU. Reproduction, storing in a retrieval system, distributing, uploading or posting online, or transmitting in anynic, mechanical, photocopying, recording, or otherwise of any part of this document, without the prior written permission of SLU, is strictlyIWERSITY

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Calculus: Early Transcendentals

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ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

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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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In each of Problems 5 through 9, verify that each given function is a solution of the differential equation. 5. ? ′′ − ? = 0; ?(?) = ? ? 6. ? ′′ + 2? ′ − 3? = 0; ?(?) = ? −3? 7. ??′ − ? = ? 2 ; ? = 3? + ? 2 8. ? ′′′′ + 4? ′′′ + 3? = ?; ?(?) = ? 3 9. ? 2? ′′ + 5?? ′ + 4? = 0; ?(?) = ? −2

DITO VOLTE
167
ll *
B/s
0( (59 14, 3:29
No service
+ Activity 1.pdf
Activity 1.
A. In each of Problems 1 through 4, determine the order and the degree of the given
differential equation; also state whether the equation is linear or nonlinear.
1. t
+ t
+ 2y = sint
2. (1+ v?)d'y
+ y = et
dt
3. + ar
+
dt2
d²y
+ y = 1
dt
dt
4.
dt
d²y
z + sin(t + y) = sin t
B. In each of Problems 5 through 9, verify that each given function is a solution of the
differential equation.
5. y" – y = 0; y(t) = et
6. y" + 2y' – 3y = 0; y(t) = e-3t
7. ty' – y = t2; y = 3t + t2
8. y" + 4y" + 3y = t; y(t) = =
9. t'y" + 5ty' + 4y = 0; y(t) = t-2
C. In each of Problems 10 through 11, determine the values of r for which the given
differential equation has solutions of the form y = et.
10. y" + y' – 6y = 0
11. y" – 3y" + 2y' = 0
D. In each of Problems 12 through 15, eliminate the arbitrary constant using the methe
you're comfortable with.
12. y = 3AX3 + 2BX² + 4Cx - D
13. x?y³ + x³y5 = C
14. y = -2C,e-3* + Cze*x
15. y = C,e-3x – 2C2e-3*
d for the exclusive use of SLU. Reproduction, storing in a retrieval system, distributing, uploading or posting online, or transmitting in any
nic, mechanical, photocopying, recording, or otherwise of any part of this document, without the prior written permission of SLU, is strictly
IWERSITY

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