rent 1(0) = 0. Calculate the a) The following differential equation is given by UTM UTM UTM ydy Use the substitution y= -a to show the above equation can be +x+ y = 0. reduced to a homogeneous equation UTM UTMUTM UTM UTM Hence find the solution for the original equation. UTM U dr UTM UTM UTM SUTM UTM b) Given an RL circuit with the equation UTM UTM UTM UTMUTM UTMUTM IP where L is the inductance, R is the resistance and 900 is the voltage L+ RI - 900, dt source. UTMUT i. Show that the solution of the above equation is UTM UTM UTM UTM UTMUTM UT I(t) - R 900 UTM TM ii. The series are connected with inductance 350 henry, and the resistance + Ce 4 UTM UTM UTM UTM is 18 ohms. Find 1(t) if the initial current I(t) at time t 1 minute. UTM MUTM TM
rent 1(0) = 0. Calculate the a) The following differential equation is given by UTM UTM UTM ydy Use the substitution y= -a to show the above equation can be +x+ y = 0. reduced to a homogeneous equation UTM UTMUTM UTM UTM Hence find the solution for the original equation. UTM U dr UTM UTM UTM SUTM UTM b) Given an RL circuit with the equation UTM UTM UTM UTMUTM UTMUTM IP where L is the inductance, R is the resistance and 900 is the voltage L+ RI - 900, dt source. UTMUT i. Show that the solution of the above equation is UTM UTM UTM UTM UTMUTM UT I(t) - R 900 UTM TM ii. The series are connected with inductance 350 henry, and the resistance + Ce 4 UTM UTM UTM UTM is 18 ohms. Find 1(t) if the initial current I(t) at time t 1 minute. UTM MUTM TM
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
Answer all questions a and b
Transcribed Image Text:rent I(0) = 0. Calculate the
UTM S UTM
a) The following differential equation is given by
UTM
UTMUTM
+x + y = 0.
UTM S UTM UTM
Use the substitution y = z - a to show the above equation can be
reduced to a homogeneous equation
UTM S UT
UTM
UTM UTM UTM
6 UTM
dz
dr
M&UTMU
Hence find the solution for the original equation.
UTM UT
UTM UTM UTM
b) Given an RL circuit with the equation
M UTM UTM
UTM
aUTM
UTM UT
where L is the inductance, R is the resistance and 900 is the voltage
dl
L+ RI = 900,
dt
UTMUTM UTM
UTMUTM
source.
i. Show that the solution of the above equation is
UTM
UTM UT
UTM
UTM S UTM UT
UTM
UTM
UTM UTM
900
I(t)
UTM S UT
UTM UTM UTM
The series are connected with inductance 350 henry, and the resistance
R
+ Ce
UTM UTM TM
is 18 ohms. Find I(t) if the initial
TM
current /(t) at time t 1 minute.
a UT
TM UTM
TMUTM
TMUT
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