and Let True or false: y" +p(x)y' +q(x)y=0 y" + p(x)y +q(x)y = g(x) ‡0 1. If y₁ and 2 solve (2), then y = y₁ - y2 solves (1); 2. If y, is a solution of (2), 2y₁ is also a solution of (2); (1) (2) 3. If y₁ and 3₂ are linearly dependent solutions of (1), then y = C₁3₁+C₂Y2 solves (1); 4. Since y₁(x) = 0 is a solution of (1), using reduction of order we can always find the general solution of (1);

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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Question
and
Let
True or false:
y” +p(x)y' +q(x)y=0
y" +p(x)y' +q(x)y = g(x) ‡ 0
1. If y₁ and 2 solve (2), then y = y₁ - y₂ solves (1);
2. If y₁ is a solution of (2), 2y₁ is also a solution of (2);
(1)
(2)
3. If y₁ and y₂ are linearly dependent solutions of (1), then y = C₁3₁ +C2Y2
solves (1);
4. Since y₁(x) == 0 is a solution of (1), using reduction of order we can
always find the general solution of (1);
Transcribed Image Text:and Let True or false: y” +p(x)y' +q(x)y=0 y" +p(x)y' +q(x)y = g(x) ‡ 0 1. If y₁ and 2 solve (2), then y = y₁ - y₂ solves (1); 2. If y₁ is a solution of (2), 2y₁ is also a solution of (2); (1) (2) 3. If y₁ and y₂ are linearly dependent solutions of (1), then y = C₁3₁ +C2Y2 solves (1); 4. Since y₁(x) == 0 is a solution of (1), using reduction of order we can always find the general solution of (1);
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