a) Find the general solution of the equation dªy dy dx² 4- x2 + 3e* - dr4 by using the method of undetermined coefficients.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Solve the given differential equation.

a) Find the general solution of the equation
d*y
d'y
4-
x2 + 3e*
-
dx4
dx?
by using the method of undetermined coefficients.
b) Given a source-free parallel RLC-circuit as
d²V
1 dV
V
dt2
+
RC dt
LC
where V is voltage of the system, R is resistance, C is capacitance and
L is inductance. If the system experiences a critically damped case
where only equal roots are present in the corresponding characteristic
equation, find the value ofL given that R= 5N and C = 0.01F. Hence,
find V (t) if V (0) = 5 and V'(0) = –100.
Transcribed Image Text:a) Find the general solution of the equation d*y d'y 4- x2 + 3e* - dx4 dx? by using the method of undetermined coefficients. b) Given a source-free parallel RLC-circuit as d²V 1 dV V dt2 + RC dt LC where V is voltage of the system, R is resistance, C is capacitance and L is inductance. If the system experiences a critically damped case where only equal roots are present in the corresponding characteristic equation, find the value ofL given that R= 5N and C = 0.01F. Hence, find V (t) if V (0) = 5 and V'(0) = –100.
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