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How did they get Y(s)? I tried, but I don't get how to convert the y' notation.

How did they get Y(s)? I tried, but I don't get how to convert the y' notation.

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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How did they get Y(s)? I tried, but I don't get how to convert the y' notation.
Solve the initial value problem below using the method of Laplace transforms. y'' - y' - 2y = 0, y(0) = -1, y'(0) = 7 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. What is the Laplace transform Y(s) of the solution y(t)? 2 3 ²2 S-2 s +1 Y(s) = Solve the initial value problem. y(t) = 2e²t - 3e (Type an exact answer in terms of e.)
Transcribed Image Text:Solve the initial value problem below using the method of Laplace transforms. y'' - y' - 2y = 0, y(0) = -1, y'(0) = 7 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. What is the Laplace transform Y(s) of the solution y(t)? 2 3 ²2 S-2 s +1 Y(s) = Solve the initial value problem. y(t) = 2e²t - 3e (Type an exact answer in terms of e.)
De 2 y"-y!-2y = 0; y(@) = -1; y'(0) = 7 ↓ ⒸL{y} = Y [₁²Y-(-1) -(7)]-[₂Y-(+)] = Y = n² Y-3 + ₂Y [₂2² +2=7]-[~Y +1]=Y=²Y+₂Y÷3 -27 +2-8-Y = 27-3 -1=227 227+1=0 DL{y} = 2²Y-₁4(0)-7² (0) = 2² Y-3 Ⓒ-2y = 0 -2Y=0 @L_{y} =nY=y(0) = Y 2- Y =227 +5. -Y = 2₂7+5-s ·+ = -2₂7 + (-5) +2 Y(2₂+1) = 2-5 Y = 2-5 22+1 A-3 дахт 2²4 +2Y-7 = 224-3 0 Y₁ =4 = 0 → Y₂-4 +2₂4 +1-2Y=0 [x+1] = + 22+1 324-3-24=0 3₂Y - 2Y = 3 Y(32-2) = 3 Y = (³) 3 -(1) 322 Y =
Transcribed Image Text:De 2 y"-y!-2y = 0; y(@) = -1; y'(0) = 7 ↓ ⒸL{y} = Y [₁²Y-(-1) -(7)]-[₂Y-(+)] = Y = n² Y-3 + ₂Y [₂2² +2=7]-[~Y +1]=Y=²Y+₂Y÷3 -27 +2-8-Y = 27-3 -1=227 227+1=0 DL{y} = 2²Y-₁4(0)-7² (0) = 2² Y-3 Ⓒ-2y = 0 -2Y=0 @L_{y} =nY=y(0) = Y 2- Y =227 +5. -Y = 2₂7+5-s ·+ = -2₂7 + (-5) +2 Y(2₂+1) = 2-5 Y = 2-5 22+1 A-3 дахт 2²4 +2Y-7 = 224-3 0 Y₁ =4 = 0 → Y₂-4 +2₂4 +1-2Y=0 [x+1] = + 22+1 324-3-24=0 3₂Y - 2Y = 3 Y(32-2) = 3 Y = (³) 3 -(1) 322 Y =
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