ONSTR the onowing mca x' (t) + 2x(t) == 0 where is an unknown function of the real variable t. 1.1) Find the general solution of (E.). 1.2) Consider now the following 1st order linear nonhomogeneou x'(t) + 2x(t) = -1. Find the general solution of (E₁).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1) Consider the following 1st order lincar homogeneous ordinary differential equation
x'(t) + 2x(1) 0
(E.)
where is an unknown function of the real variable t.
1.1) Find the general solution of (E.).
1.2) Consider now the following 1st order linear nonhomogeneous ordinary differential equation
x'(t) + 2x(1)
-
-1.
(E₁)
Find the general solution of (E₁).
2) Consider the equation 212y" + 3ty' - y = 0.
1
2.1) Verify that yı(t)
(t > 0) is a solution of the above equation.
t'
2.2) Find a second linearly independent solution using Method of Reduction of Order.
Transcribed Image Text:1) Consider the following 1st order lincar homogeneous ordinary differential equation x'(t) + 2x(1) 0 (E.) where is an unknown function of the real variable t. 1.1) Find the general solution of (E.). 1.2) Consider now the following 1st order linear nonhomogeneous ordinary differential equation x'(t) + 2x(1) - -1. (E₁) Find the general solution of (E₁). 2) Consider the equation 212y" + 3ty' - y = 0. 1 2.1) Verify that yı(t) (t > 0) is a solution of the above equation. t' 2.2) Find a second linearly independent solution using Method of Reduction of Order.
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