5_2-Clicker-Second Order Linear ODEs

# 5_2-Clicker-Second Order Linear ODEs - where ω is...

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1 How many initial conditions are required to fully determine the particular solution to a 2nd order differential equation?

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2 How many initial conditions are required to fully determine the general solution to a 2nd order linear differential equation?
How many initial conditions are required to fully determine the particular solution to a 2nd order differential equation? A) 1 B) 2 C) 3 D) 4 E) Cannot tell

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4 Since cos(ωt) and cos(-ωt) are both solutions of can we express the general solution as y(t)=C1cos(ωt) + C2cos(-ωt) ? A) yes B) no C) ???/depends Ý Ý x ( t ) =-ϖ 2 x ( t )
5 Ý Ý x ( t ) =-ϖ 2 x ( t ) What is the general solution to the ODE

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Unformatted text preview: where ω is some (known) constant? A) x ( t ) = A cos ϖ t + B sin t B) x ( t ) = Ce i t + De-i t C) x ( t ) = A cos t + B sin t + Ce i t + De-i t D) None of these is fully general! E) More than one of these is fine Challenge question: Is there any OTHER general form for this solution? 6 Are sin(x) and cos(x) linearly independent? A) yes B) no C) ??? 7 Are eiωx and e-iωx linearly independent? A) yes B) no C) It depends on omega D) ??? 8 Are e-t and e-4t linearly independent? A) yes B) no C) ???...
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## This note was uploaded on 02/27/2012 for the course PHYSICS 2210 taught by Professor Stevepollock during the Spring '11 term at Colorado.

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5_2-Clicker-Second Order Linear ODEs - where ω is...

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