182_pdfsam_math 54 differential equation solutions odd

182_pdfsam_math 54 differential equation solutions odd -...

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Chapter 4 3. The auxiliary equation, r 2 6 r +10=0,hasroots r = ( 6 ± 6 2 40 ) / 2=3 ± i .So α =3, β =1 ,and z ( t )= c 1 e 3 t cos t + c 2 e 3 t sin t is a general solution. 5. This diferential equation has the auxiliary equation r 2 +4 r +6 = 0. The roots oF this auxiliary equation are r = ( 4 ± 16 24 ) / 2= 2 ± 2 i .W es e etha t α = 2and β = 2. Thus, a general solution to the diferential equation is given by w ( t )= c 1 e 2 t cos 2 t + c 2 e 2 t sin 2 t. 7. The auxiliary equation For this problem is given by 4 r 2 4 r +26=0 2 r 2 2 r +13=0 r = 2 ± 4 104 4 = 1 2 ± 5 2 i. ThereFore, α =1 / 2and β =5 / 2. Thus, a general solution is given by y ( t )= c 1 e t/ 2 cos ± 5 t 2 ² + c 2 e t/ 2 sin ± 5 t 2 ² . 9. The associated auxiliary equation, r 2
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.

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