QUESTION 1 s UTM a) The following differential equation is given by UTM 5 UTM 6 UTM Use the substitution y² = z – x to show the above equation can be reduced to a homogeneous equation dy +x + y? = 0. U UTM & UTM dr 5 UTM 6 UTM UTM & UTM TM & UTM 5 UT Hence find the solution for the original equation. dx 6 UTM x – z° M 8 UTM 5 UTM ITM
QUESTION 1 s UTM a) The following differential equation is given by UTM 5 UTM 6 UTM Use the substitution y² = z – x to show the above equation can be reduced to a homogeneous equation dy +x + y? = 0. U UTM & UTM dr 5 UTM 6 UTM UTM & UTM TM & UTM 5 UT Hence find the solution for the original equation. dx 6 UTM x – z° M 8 UTM 5 UTM ITM
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:QUESTION 1
UTM
a) The following differential equation is given by
5 UTM
5 UTM
6 UTM
lip
+ x + y? = 0.
Use the substitution y? = z – x to show the above equation can be
U 6 UTM 5 UTM
dz
reduced to a homogeneous equation
5 UTM & UT
6 UTM
5 UTM
5 UTM
TM & UTM 5 UT
Hence find the solution for the original equation.
x + z
d.x
x – z
&UTM & UT
5 UTM
b) Given an RL circuit with the equation
M 8 UTM 6 UTM
UTM
5 UTM
* ITM UT
&UTM
IP
L + RI = 900,
dt
where L is the inductance, R is the resistance and 900 is the voltage
UTM UTM 5 U1.
source.
i. Show that the solution of the above equation is
S UTM
& UTM UT
& UTM
UTM
5 UTM & UTM UTM
900
I(t) =
5 UTM UT
TM
+ Ce-#.
R
ii. The series are connected with inductance 350 henry, and the resistance
5 UTM& UTM 5 UTM
is 18 ohms. Find I(t) if the initial current I(0) = 0. Calculate the
current I(t) at time t = 1 minute.
"M 6 UT
TM
5 UTM
TM
UTM & UT
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