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posted by  comet1 on 7/24/2008 7:37:45 AM  |  status: Live  

laplace transform method ONLYplease!

Course Textbook Chapter Problem
Differential Equations N/A N/A N/A
Question Details:
solve the initial value problem using the method of laplace transforms ONLY, even though it can be done by another method (undetermined coefficients)  
 
y'' - 2y' +5y =0,  y(0) = 2,   y'(0) = 4

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posted by Altair on 7/24/2008 7:57:09 AM  |  status: Live
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comet1's comment:
"thanks, but I needed to see this by the method of laplace transforms, even though it can be done by another method (undetermined coefficients) "
Response Details:
the charactericstic equation is:
 
m2 -2m + 5 =0
 
 
the egeneral solution is:
 
y=c1e(1+2i)x + c2e(1-2i)x  = ex[c1e2ix + c2e-2ix  ]
 
y(0)=2=c1 + c2
 
y'(x) = ex[c1e2ix + c2e-2ix  ] + ex[2ic1e2ix -2ic2 e-2ix]
y'(0) = c1 + c2 + 2ic1 -2ic2 = 4
 
solve c1 and c2 you will get the solution.
 

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