Complete the solution to the following differential equation. y + 4y + 3y = 16e' y(0) = 0, y (0) = 1 Applying the Laplace transform in both sides we get\\ 1 s?Y(s) – sy(0) – y (0) + 4[s¥(s) – y(0)] + 3Y(s) = 16 · 1 S - 16 s?Y(s) – 1 + 4sY(s) + 3Y(s) S - 1 16 Y(s)[s + 4s + 3] = 1 + S – 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Complete the solution to the following differential equation.
y" + 4y + 3y = 16e' y(0) = 0,
y (0) = 1
Applying the Laplace transform in both sides we get\\
1
s?Y(s) – sy(0) – y (0) + 4[s¥(s) – y(0)] + 3Y(s) = 16 ·
1
S -
16
s?Y(s) – 1 + 4sY(s) + 3Y(s)
1
16
Y(s)[s + 4s + 3] = 1 +
S – 1
Transcribed Image Text:Complete the solution to the following differential equation. y" + 4y + 3y = 16e' y(0) = 0, y (0) = 1 Applying the Laplace transform in both sides we get\\ 1 s?Y(s) – sy(0) – y (0) + 4[s¥(s) – y(0)] + 3Y(s) = 16 · 1 S - 16 s?Y(s) – 1 + 4sY(s) + 3Y(s) 1 16 Y(s)[s + 4s + 3] = 1 + S – 1
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