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Verify whether the general solution \(y=e^xcosx\) does satisfy the D.E.  Y”  -2Y’ + 2Y= 0

 Aug 4, 2017
edited by zzzzz  Aug 4, 2017
 #1
avatar+102422 
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y = e^x cos (x)

 

y '  = e^x cos(x)  - e^x sin(x)

 

y "  = e^x cos (x)  - e^x sin (x)  - e^x sin (x)  - e^x cos(x)  =  -2 e^x sin (x)

 

So

 

y"   -  2y' + 2y  =

 

 -2 e^x sin (x)  - 2 [  e^x cos(x)  - e^x sin(x) ] + 2 [ e^x cos(x) ]   =  0

 

 

 

cool cool cool

 Aug 4, 2017

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