1. Let the following higher order differential equation (1) y" – 2 y" – 3y = 3e. 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 = 3e. 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:Excrcise 1:
1. Let the following higher order differential equation
(1)
y" – 2 y" – 3 y = 3er.
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(3.r) + 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" + 2xy' – 2y = 0, z € (0, 0).
Let yı (1) = a 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" - 5zy - y = 0. about the ordinary point 0.
(Find ag, . as).
2. Find and classify the singular points of the differential equation r (r- 1) y" + ry +y = 0.
Exercise 3:
dri(t)
dt
= 21 +a2 + 3r3
1. Solve the homogeneous linear system of D. E. (S)
2x2 + 2x3
%3D
dt
dra(t)
dt
3r3.
2. Find a particular solution, using undetermined coefficients, for the following nonhomogeneous
-(: :)x+(*").
e + 2t
the system of differential equations X' =
1
3t
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