10. Use the method reduction of order to find a second solution y₂(-) to each of the following differential equations given y₁(-). (a) t²y" — 4ty' + 6y = 0, t > 0, y₁(t) = t² (b) t²y" +3ty' + y = 0, t > 0, y₁(t) = t−¹
10. Use the method reduction of order to find a second solution y₂(-) to each of the following differential equations given y₁(-). (a) t²y" — 4ty' + 6y = 0, t > 0, y₁(t) = t² (b) t²y" +3ty' + y = 0, t > 0, y₁(t) = t−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
Transcribed Image Text:10. Use the method reduction of order to find a second solution y₂(-)
to each of the following differential equations given y₁ (-).
(a) t²y" - 4ty' + 6y = 0, t > 0, y₁ (t) = t²
(b) t²y" + 3ty' + y = 0, t > 0, y₁ (t) = t−¹
11. Use Abel's theorem to find a second solution y2(-) to each of the
following differential equations given y₁(-).
(a) (x - 1)y" - xy' + y = 0. x > 1, y₁(x) = eª
(b) x²y" + xy' + (x² − 0.25)y = 0, x > 0, y₁ (x):
= I
-1/2 sin(x)
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You post 4 separated questions, as per our guideline we can solve only first question.
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However i solve both questions of #10.
Given equation is of second order differential equation, using the given solution we find an equation of order 1. Then solve it.
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