let y'' +p(x)y' +q(x)y =0 (1)and y′′ +p(x)y′ +q(x)y =g(x)≠0 (2)True or false:If y1 and y2 solve(2), then y= y1-y2 solves(1);If y1 is a solution of (2), 2y1 is also a solution of (2);If y1 and y2 are linearly dependent solutions of (1), then y = c1y1 + c2y2 solves (1);Since y1(x) ≡ 0 is a solution of (1), using reduction of order we can always find the general solution of (1);

In this question, we have to check the given statements either these are true or false. y'' +p(x)y'…

Answered: y'' +p(x)y' +q(x)y =0…

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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let

y'' +p(x)y' +q(x)y =0 (1)

and y′′ +p(x)y′ +q(x)y =g(x)≠0 (2)

True or false:

If y₁ and y₂ solve(2), then y= y₁-y₂ solves(1);
If y₁ is a solution of (2), 2y₁ is also a solution of (2);
If y₁ and y₂ are linearly dependent solutions of (1), then y = c₁y₁ + c₂y₂ solves (1);
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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