wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Using Laplace transform, solve
d2ydt2+4y=12t
Given that y = 0 and dy/dt = 9 at t = 0.

A
a
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
b
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
c
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
d
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D d
d2ydt2+4y=12t
By taking Laplace transform of LHS and RHS and using the property of derivatives of transform L[fn(t)]=snF(S)sn1f(0)sn2f(0)......fn1(0) we get subsidiary equation as :
(s2+4)Ysy(0)y(0=12s2
(s2+4)Y=12s2+5(0)+9
Y=12s2(s2+4)+9s2+4
Y=3s2+3s2+4+9s2+4
Y=3s2+6s2+4
y(t)=L1(Y)
y(t)=L1(3s2)+L1(6s2+22)
y(t)=3t+3sin2t

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
What Sound Really Is
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon