1. Here are three second-order differential equations with initial conditions: a) y(x): y-3y-4y=x²-5 y(1) = 0, y' (1)=2 In each case: (i) Find the complementary function. (ii) Find the particular integral. (iii) Find the solution that satisfies the initial conditions given. (iv) Rewrite the equation as a system of two first-order differential equations together with the appropriate initial conditions.
1. Here are three second-order differential equations with initial conditions: a) y(x): y-3y-4y=x²-5 y(1) = 0, y' (1)=2 In each case: (i) Find the complementary function. (ii) Find the particular integral. (iii) Find the solution that satisfies the initial conditions given. (iv) Rewrite the equation as a system of two first-order differential equations together with the appropriate initial conditions.
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:1.
Here are three second-order differential equations with initial conditions:
n)
y(x):
y-3y-4y=x²-5
y(1) = 0,
y (1)=2
In each case:
(1)
Find the complementary function.
(ii)
Find the particular integral.
Find the solution that satisfies the initial conditions given.
(iv) Rewrite the equation as a system of two first-order differential equations together
with the appropriate initial conditions.
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