y" + 4y = 41² y (0) = 0, 4t + 10; y' (0) = 3 -
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Number 8
Transcribed Image Text:In Problems 1-14, solve the given initial value problem using
the method of Laplace transforms.
1. y" - 2y + 5y = 0;
y(0) = 2,
y(0) = -2.
y(0)
y(0) -1,
2.
y" - y' - 2y = 0;
3. y" + 6y' +9y = 0;
4. y" + 6y' + 5y = 12e¹;
5. w"+w= ² + 2;
6. y"-4y' + 5y = 4e³t;
7. y" - 7y' +10y = 9 cost + 7 sint;
y (0) = 5,
y' (0) = -4
8. y" + 4y = 4t² − 4t + 10 ;
y(0) = 0,
y' (0) = 3
9. z" +5z' - 6z
z(1) = -1,
10. y" - 4y = 4t - 8e-²¹;
=
= −1,
w(0) = 1,
y (0) = 2,
21e¹-1;
z' (1) = 9
y(0) =
=
0,
y' (0) = 4
y' (0)
= 5
y' (0) =
y'(0) = 7
w' (0)
= 6
= -1
y' (0) = 7
y' (0) = 5
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