6. 5. Find the general solution of the equation xy" + 2y' + xy = 0, if we know that y₁ = solution. COS X X is a
6. 5. Find the general solution of the equation xy" + 2y' + xy = 0, if we know that y₁ = solution. COS X X is a
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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4/5: Please solve the following differential equations marked with a red circle.
![4. In each case, find a second order, linear, homogeneous ODE that has the given pair of functions
as its solutions. Then show that the pair forms a fundamental set of solutions.
2e³t5e-t, y₂ = 11e-t
(b) y₁ = cos(πt), y₂ =
=sin(at)
(c) Y₁ = e2t cos(5t), y2 = e²t sin(5t)
(d) y₁ = e³t, y₂ = te³t
(a) yı
=
5. Find the general solution of the equation xy" + 2y + xy = 0, if we know that y₁ =
solution.
COS X
X
is a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F862d597a-ccd1-4202-ba0c-cb7527992470%2F7a9c5d75-3b23-41b4-b597-333d7dd92fe4%2Fq6af0g4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. In each case, find a second order, linear, homogeneous ODE that has the given pair of functions
as its solutions. Then show that the pair forms a fundamental set of solutions.
2e³t5e-t, y₂ = 11e-t
(b) y₁ = cos(πt), y₂ =
=sin(at)
(c) Y₁ = e2t cos(5t), y2 = e²t sin(5t)
(d) y₁ = e³t, y₂ = te³t
(a) yı
=
5. Find the general solution of the equation xy" + 2y + xy = 0, if we know that y₁ =
solution.
COS X
X
is a
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