= eat. Use 4. Consider the equation x" - 2ax' + a²x = 0, which has solution x = reduction of order to find a second independent solution. (This shows the origin of the teat solution in a second-order linear equation with constant coefficients, in the real, equal eigenvalue case.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please do number 4
is a solution.
eat. Use
4. Consider the equation x" - 2ax' + a²x = 0, which has solution x =
reduction of order to find a second independent solution. (This shows the
origin of the teat solution in a second-order linear equation with constant
coefficients, in the real, equal eigenvalue case.)
5. One solution of
t+2
x"
t
is x₁ (t) = t. Find a second independent solution.
·x² +
t + 2
t²
- x = 0
Transcribed Image Text:is a solution. eat. Use 4. Consider the equation x" - 2ax' + a²x = 0, which has solution x = reduction of order to find a second independent solution. (This shows the origin of the teat solution in a second-order linear equation with constant coefficients, in the real, equal eigenvalue case.) 5. One solution of t+2 x" t is x₁ (t) = t. Find a second independent solution. ·x² + t + 2 t² - x = 0
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