1. Let the following higher order differential equation (1) y" - 2 y" – 3y = 3 e. Determine the general solution of (1) using variation of parameters method for particular solution.
1. Let the following higher order differential equation (1) y" - 2 y" – 3y = 3 e. Determine the general solution of (1) using variation of parameters method for particular solution.
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:Exercise 1:
1. Let the following higher order differential equation
(1) y" – 2 y" – 3 y = 3 er.
Determine the general solution of (1) using variation of parameters method for
particular solution.
2. Consider the following Differential Equation
(2) y" – 2 y" – 3 y = cos(3r) + e".
Determine the form of a particular solution by the undetermined coefficients method and
write a general solution of (2).
3. Let the second order Differential Equation (3) y" + 2 ry – 2 y = 0, r € (0, x).
Let yı(x) = r a first solution of (3), use the method of reduction of order to find a second
solution of (3).
Exercise 2 :
1. Determine a series solutions of the D. E. y" – 5x y' – y = 0. about the ordinary point 0.
(Find ag. . as).
2. Find and classify the singular points of the differential equat ion r(r – 1)y" + ry +y = 0.
Exercise 3 :
dri(t)
da = r1+ 12 + 3r3
dra(t)
dr alt)
1. Solve the homogeneous linear system of D. E. (S)
2r2 + 2r3
3r3.
%3D
dt
2. Find a particular solution, using undetermined coefficients, for the following nonhomogeneous
1 2
13
x+ (*,").
e + 2t
the system of differential equations X' = (G
3t
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