Solve the following Cauchy–Euler equations by using the
Chapter 4, Problem 24E(choose chapter or problem)
Solve the following Cauchy-Euler equations by using the substitution described in Problem 23 to change them to constant coefficient equations, finding their general solutions by the methods of the preceding sections, and restoring the original independent variable
(a) \(t^{2} y^{\prime \prime}+t y^{\prime}-9 y=0\)
(b) \(t^{2} y^{\prime \prime}+3 t y^{\prime}+10 y=0\)
(c) \(t^{2} y^{\prime \prime}+3 t y^{\prime}+y=t+t^{-1}\)
(d) \(t^{2} y^{\prime \prime}+t y^{\prime}+9 y=-\tan (3 \ln t)\)
Equation Transcription:
Text Transcription:
t^2y''+ty'-9y=0
t^2y''+3ty'+10y=0
t^2y''+3ty'+y=t+t^-1
t^2y''+ty'+9y=-tan(3 ln t)
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