PLEASE SHOW ALL STEPS CLEARLY AND COME TO A COMPLETE CORRECT ANSWER THANK YOU!!!
Use Laplace to solve di(t)/dt+9i(t)=3u(t) with i(0 - )=2A. What is i(t) ?
Hint: Laplace of (di(t)/dt)= SI ( S )-i(0 - )
A. i(t)=(5/3)u(t)-(1/3)e 9t u(t)
B. i(t)=(1/3)u(t)+(5/3)e -9t u(t)
C. i(t)=(1/3)u(t)-(5/3)e 9t u(t)
D. i(t)=(5/3)u(t)+(1/3)e -9t u(t)
Solution
Given differential equation is  di(t)/dt+9i(t)=3u(t)
Given i(0 -)=2A
now applying laplace transform to the given equation we have
I(s)-I(0-) +9I(s)=3/s
now substitute the given value I(0-)=2A
s.I(s)-2 +9I(s)=3/s
I(s)[s+9]=(3/s) +2
I(s)[s+9]=(2s+3)/s
I(s)={2s(s+1.5)/s}/(s+9)
=2s(s+1.5)/[s(s+9)] -----------------(1)
now apply partial fractions to the above equation we have
2s(s+1.5)/[s(s+9)] =A/s + B/(s+9)
2s(s+1.5)=A(s+9)+Bs
at s=0
A=3/9 =1/3
and at s=-9
B=5/3
resultant inverse laplace transform of equation (1) is
i(t)= (1/3) u(t) +(5/3) e^(-9t) u(t)
now for the Given problem option B. i(t)=(1/3)u(t)+(5/3)e-9t u(t) is correct answer
.
Web & Social Media Analytics Previous Year Question Paper.pdf
PLEASE SHOW ALL STEPS CLEARLY AND COME TO A COMPLETE CORRECT ANSWER TH.docx
1. PLEASE SHOW ALL STEPS CLEARLY AND COME TO A COMPLETE CORRECT
ANSWER THANK YOU!!!
Use Laplace to solve di(t)/dt+9i(t)=3u(t) with i(0 -
)=2A. What is i(t) ?
Hint: Laplace of (di(t)/dt)= SI ( S )-i(0 -
)
A. i(t)=(5/3)u(t)-(1/3)e 9t
u(t)
B. i(t)=(1/3)u(t)+(5/3)e -9t
u(t)
C. i(t)=(1/3)u(t)-(5/3)e 9t
u(t)
D. i(t)=(5/3)u(t)+(1/3)e -9t
u(t)
Solution
Given differential equation is  di(t)/dt+9i(t)=3u(t)
Given i(0 -)=2A
now applying laplace transform to the given equation we have
I(s)-I(0-) +9I(s)=3/s
now substitute the given value I(0-)=2A
s.I(s)-2 +9I(s)=3/s
I(s)[s+9]=(3/s) +2
I(s)[s+9]=(2s+3)/s
I(s)={2s(s+1.5)/s}/(s+9)
=2s(s+1.5)/[s(s+9)] -----------------(1)
2. now apply partial fractions to the above equation we have
2s(s+1.5)/[s(s+9)] =A/s + B/(s+9)
2s(s+1.5)=A(s+9)+Bs
at s=0
A=3/9 =1/3
and at s=-9
B=5/3
resultant inverse laplace transform of equation (1) is
i(t)= (1/3) u(t) +(5/3) e^(-9t) u(t)
now for the Given problem option B. i(t)=(1/3)u(t)+(5/3)e-9t u(t) is correct answer
![PLEASE SHOW ALL STEPS CLEARLY AND COME TO A COMPLETE CORRECT
ANSWER THANK YOU!!!
Use Laplace to solve di(t)/dt+9i(t)=3u(t) with i(0 -
)=2A. What is i(t) ?
Hint: Laplace of (di(t)/dt)= SI ( S )-i(0 -
)
A. i(t)=(5/3)u(t)-(1/3)e 9t
u(t)
B. i(t)=(1/3)u(t)+(5/3)e -9t
u(t)
C. i(t)=(1/3)u(t)-(5/3)e 9t
u(t)
D. i(t)=(5/3)u(t)+(1/3)e -9t
u(t)
Solution
Given differential equation is  di(t)/dt+9i(t)=3u(t)
Given i(0 -)=2A
now applying laplace transform to the given equation we have
I(s)-I(0-) +9I(s)=3/s
now substitute the given value I(0-)=2A
s.I(s)-2 +9I(s)=3/s
I(s)[s+9]=(3/s) +2
I(s)[s+9]=(2s+3)/s
I(s)={2s(s+1.5)/s}/(s+9)
=2s(s+1.5)/[s(s+9)] -----------------(1)](https://image.slidesharecdn.com/pleaseshowallstepsclearlyandcometoacompletecorrectanswerth-230131015129-20f540cc/85/PLEASE-SHOW-ALL-STEPS-CLEARLY-AND-COME-TO-A-COMPLETE-CORRECT-ANSWER-TH-docx-1-320.jpg)
![now apply partial fractions to the above equation we have
2s(s+1.5)/[s(s+9)] =A/s + B/(s+9)
2s(s+1.5)=A(s+9)+Bs
at s=0
A=3/9 =1/3
and at s=-9
B=5/3
resultant inverse laplace transform of equation (1) is
i(t)= (1/3) u(t) +(5/3) e^(-9t) u(t)
now for the Given problem option B. i(t)=(1/3)u(t)+(5/3)e-9t u(t) is correct answer](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)