Solve the following initial value problems using Laplace transform and plase your solution using the indicated format +D+2)y=5+4sin(t): 1. (D³ +2D² 2. (D²+5D+6)y=5+3e³: y(0) = 3, y(0) = 1, y"(0) = 2 y(0) = 5, y(0) = 0 3. (D² +6D+4) y = 6e² +41² : y(0) = 4, y(0) = 2

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
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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Solving Differential Equation by Laplace Transform
Solve the following initial value problems using Laplace transform and plase your solution using the indicated format:
1. (D³ +2D² +D+2) y = 5 + 4sin(t): y(0) = 3, y(0) = 1, y"(0) = 2
2. (D² +5D+6)y=5+3e³¹: y(0) = 5, y(0) = 0
3. (D² +6D+4) y = 6e² + 4t² : y(0) = 4, y(0) = 2
Required:
1. Use laplace transforms
2. Find the laplace transform of the entire equation and set it implicitly (eqn1, eq2,eqn3).
3. Plugin the initial conditions and save it as L_Eq1,L_Eq2, L_Eq3
4. Find the solution to the equation (ysoln1, ysoln2, ysoln3)
Transcribed Image Text:Solving Differential Equation by Laplace Transform Solve the following initial value problems using Laplace transform and plase your solution using the indicated format: 1. (D³ +2D² +D+2) y = 5 + 4sin(t): y(0) = 3, y(0) = 1, y"(0) = 2 2. (D² +5D+6)y=5+3e³¹: y(0) = 5, y(0) = 0 3. (D² +6D+4) y = 6e² + 4t² : y(0) = 4, y(0) = 2 Required: 1. Use laplace transforms 2. Find the laplace transform of the entire equation and set it implicitly (eqn1, eq2,eqn3). 3. Plugin the initial conditions and save it as L_Eq1,L_Eq2, L_Eq3 4. Find the solution to the equation (ysoln1, ysoln2, ysoln3)
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,