(c) Consider the second order linear differential equation d'y dy +8 + 16y= 2x +3 dx² dx (i) Find the general solution of the associated homogeneous equation: d²y dx² dy + 8- + 16y 0. dx 39 == 8 (*) (ii) Find the particular solution of the inhomogeneous equation (*). (iii) Find the specific solution of the inhomogeneous equation (*) subject to the initial conditions y = 17 and 1 when x = 0.
(c) Consider the second order linear differential equation d'y dy +8 + 16y= 2x +3 dx² dx (i) Find the general solution of the associated homogeneous equation: d²y dx² dy + 8- + 16y 0. dx 39 == 8 (*) (ii) Find the particular solution of the inhomogeneous equation (*). (iii) Find the specific solution of the inhomogeneous equation (*) subject to the initial conditions y = 17 and 1 when x = 0.
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:(c) Consider the second order linear differential equation
d²y
dy
+8.
dx²
dx
(i) Find the general solution of the associated homogeneous equation:
8
d²y
dx²
and dy
dx
+ 16y= 2x +3
dy
+ 8- + 16y = 0.
dx
(ii) Find the particular solution of the inhomogeneous equation (*).
(iii) Find the specific solution of the inhomogeneous equation (*) subject to the initial
39 when x = 0.
conditions y =
(*)
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