Differential equations 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 forparticular 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 andwrite 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 secondsolution 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 + 3r31. Solve the homogeneous linear system of D. E. (S)2x2 + 2x3%3Ddtdra(t)dt3r3.2. Find a particular solution, using undetermined coefficients, for the following nonhomogeneous-(: :)x+(*").e + 2tthe system of differential equations X' =13t

Given y'''-2y''-3y' = 3e5x 1The auxiliary equation for homogeneous…

Answered: 1. Let the following higher order…

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Differential equations

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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ISBN:

9780470458365

Author:

Erwin Kreyszig

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Wiley, John & Sons, Incorporated