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The Bessel equation of order one-half, t²y''+ty' + + [ 2² - 17 ) y = solutions, y₁=t-1/² cos (t) and y₂ = t1/2 sin (t). Find a general solution to the nonhomogeneous equation below. Py" +ty + (2-1)y=f/², t>c 0 y=0, t> 0, has two linearly independent y(t) = 15/2 - 6t¹/2 +c₁t¯1/2 cos (t)+c₂t¹/2 sin (t)

The Bessel equation of order one-half, t²y''+ty' + + [ 2² - 17 ) y = solutions, y₁=t-1/² cos (t) and y₂ = t1/2 sin (t). Find a general solution to the nonhomogeneous equation below. Py" +ty + (2-1)y=f/², t>c 0 y=0, t> 0, has two linearly independent y(t) = 15/2 - 6t¹/2 +c₁t¯1/2 cos (t)+c₂t¹/2 sin (t)

Advanced Engineering Mathematics
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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The Bessel equation of order one-half, ty" + ty' + [2² - 1) -)y=0, y = 0, t > 0, has two linearly independent ₁ 4 1/2 sin (t). Find a general solution to the nonhomogeneous solutions, y₁ = t equation below. -1/2 cos (t) and y₂ = t Ry" +ty² + (2-1)y=10¹², 10 9/2 y(t) = t +5/2_6t¹/2 +c₁t¯1/2 - cos (t) + C₂t¯1/2 sin (t)
Transcribed Image Text:The Bessel equation of order one-half, ty" + ty' + [2² - 1) -)y=0, y = 0, t > 0, has two linearly independent ₁ 4 1/2 sin (t). Find a general solution to the nonhomogeneous solutions, y₁ = t equation below. -1/2 cos (t) and y₂ = t Ry" +ty² + (2-1)y=10¹², 10 9/2 y(t) = t +5/2_6t¹/2 +c₁t¯1/2 - cos (t) + C₂t¯1/2 sin (t)
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