Solve the folowing differential equations using Laplace transform method. (1) y"+4y'+5y =50, y(0)=5, y '(0) =-5 (2) y"+16y = 48(t -z), y(0) =-1, y '(0) = 0 (3) y"-y'-2y = 12u (1 – z)sint, y (0) = 1, y'(0) =-1 (4) y"+3y'+2y =2u (t –2), y(0)=0, y'(0) =0 (5) y"+3y'+2y =f (t), y(0)=1, y (0) = 0 %3D %3D where f(1)=0, 0 (6) y"+5y'+6y =u (1 – z)cos(t – 7), y (0) =1, y'(0) = 0 (7) y"-5y'+6y =tu (t-1), y (0)=0, y'(0)=0 (8) y"-5y'+6y =1+fu(t -2). y(0)=0, y'(0) =1 (9) y"-5y'+10y =tu(t – 3). y(0) =1, y'(0) =1 (10) y"+2y'+10y =e*u (t –1), y (0) = -1, y'(0) =0 (11) y"-y'-2y =e u (t -1), y (0)=1, y'(0) =0 (12) y"-3y'+2y = 4e, y(0)=-3, y'(0) = 5 (13) y"-y'-2y =20sin 2r, y(0)=1, y'(0)=2 y"+3y'+2y =2(1 +1 +1). y(0) =2, y'(0) =0 %3D (15) y"+2y'+5y =e*sint, y(0)=0, y'(0) =1 (16) y +ydt = 1-e (17) dt dy +2y +[ydt = sint, y(0)=1 d'ydy di +2y =t8(1-1). y (0) =0, y'(0)=0 (18 +3 dt 0<1 <1 (19) y"+4y =f (). y(0)=0, y'(0) =1 where f()=- t>1
Solve the folowing differential equations using Laplace transform method. (1) y"+4y'+5y =50, y(0)=5, y '(0) =-5 (2) y"+16y = 48(t -z), y(0) =-1, y '(0) = 0 (3) y"-y'-2y = 12u (1 – z)sint, y (0) = 1, y'(0) =-1 (4) y"+3y'+2y =2u (t –2), y(0)=0, y'(0) =0 (5) y"+3y'+2y =f (t), y(0)=1, y (0) = 0 %3D %3D where f(1)=0, 0 (6) y"+5y'+6y =u (1 – z)cos(t – 7), y (0) =1, y'(0) = 0 (7) y"-5y'+6y =tu (t-1), y (0)=0, y'(0)=0 (8) y"-5y'+6y =1+fu(t -2). y(0)=0, y'(0) =1 (9) y"-5y'+10y =tu(t – 3). y(0) =1, y'(0) =1 (10) y"+2y'+10y =e*u (t –1), y (0) = -1, y'(0) =0 (11) y"-y'-2y =e u (t -1), y (0)=1, y'(0) =0 (12) y"-3y'+2y = 4e, y(0)=-3, y'(0) = 5 (13) y"-y'-2y =20sin 2r, y(0)=1, y'(0)=2 y"+3y'+2y =2(1 +1 +1). y(0) =2, y'(0) =0 %3D (15) y"+2y'+5y =e*sint, y(0)=0, y'(0) =1 (16) y +ydt = 1-e (17) dt dy +2y +[ydt = sint, y(0)=1 d'ydy di +2y =t8(1-1). y (0) =0, y'(0)=0 (18 +3 dt 0<1 <1 (19) y"+4y =f (). y(0)=0, y'(0) =1 where f()=- t>1
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
Transcribed Image Text:Solve the folowing differential equations using Laplace transform method.
(1) y"+4y'+5y = 50, y(0) = 5, y'(0) =-5
(2) y"+16y =48(t –7), y(0) =-1, y'(0) =0
(3) y"-y'-2y = 12u (1 -7)sint, y (0) = 1, y'(0) =-1
%3D
(4) y"+3y'+2y =2u (t –2), y(0)=0, y'(0) =0
(5) y"+3y'+2y =f (t). y(0)=1, y'(0) = 0
where f (t)=0, 0<t <n; f(t)=sin 21, t>t
(6) y"+5y'+6y =u (1 – x)cos(1 - 7), y (0) =1, y'(0) =0
(7) y"-5y'+6y =tu(t -1), y (0)=0, y'(0) =0
(8) y"-5y'+6y =l+tu(t -2). y(0)=0, y '(0)=1
(9) y"-5y'+10y =tu(1 -3), y(0) =1, y'(0) = 1
(10) y"+2y'+10y =e*u (t -1), y (0) =-1, y'(0) = 0
(11) y"-y'-2y =e u(1-1). y(0) =1, y'(0) = 0
(12) y"-3y'+2y = 4e, y (0) =-3, y'(0) = 5
(13) y"-y'-2y 20sin 2r, y(0)=1, y'(0)=2
H y"+3y'+2y =2(1² +1 +1), y(0) =2, y'(0) = 0
(15) y"+2y'+5y =e*sint, y(0) = 0, y'(0) =1
(16) y +Jydt =1-e
(17)
+2y +Jydt sint, y(0)=1
%3D
d'y
(18)
dt
+2y =18(1-1). y (0) =0, y'(0) =0
dt
0<1 <1
(19) y"+4y =f (t), y(0)=0, y'(0) =1 where f(t)=
t>1
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
