y'' +4y' +5y=3e-2x cos x solve the above differential equation

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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 y'' +4y' +5y=3e-2x cos x

solve the above differential equation

 

Expert Solution
Step 1

The given differential equation is ,

     y''+4y'+5y=3e-2xcosx

then the solution is given by , 

               y(x) = yc+yp

; Where  yc complementary function        and   yp particular solution .

(.).   1f(D)eaxV  =   eax1f(D+a)V         

 ; where  V is a function of  'x' .

(.)      1f(D2)cos(ax) = 1f(-a2)cos(ax) 

  provided  f(-a2)  0 

case of failure :  If  f(-a2) = 0 , then                 1f(D2)cos(ax) = xf'(-a2)cos(ax) 

  provided  f'(-a2)   0

 

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