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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 +41² : 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

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 +41² : 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

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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DIFFERENTIAL EQUATION

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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+3e³t: y(0) = 5, y(0) = 0 3. (D²+6D+4) y = 6e²+ 41² : 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+3e³t: y(0) = 5, y(0) = 0 3. (D²+6D+4) y = 6e²+ 41² : 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)
1 syms y(t), t Dy=diff(y); 3 D2y=diff(y, 2); 4 D3y=diff(y, 3); 5
Transcribed Image Text:1 syms y(t), t Dy=diff(y); 3 D2y=diff(y, 2); 4 D3y=diff(y, 3); 5
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