Give the general solution of the differential equation 4x p"+4y'+ 20y =2 e** cos( 2x) 1 e** cos( 2x) + 1 e** sin (2 x) + cos( 2 x) C, + C, sin(4 x) 4x a) O y= 30 4x 60 1 4x 1 4x b) O y =C, e"cos(2 x) + C, e** sin( 2 x) + e"cos( 2 x) + 30 e" sin(2x) 60 1 e** cos( 2x) 4x 4x c) O y=C, e*cos( 2 x) + C, e** sin(2x) 30 60 e" sin(2x) 1 1 e** sin (2 x) -2x -2x 4x 4x d) O y=C, e *cos(4 x) + C, e +C,e*sin(4x) + e" cos( 2 x) + 30 60 1 e*"cos( 2 x) 30 -2x 1 -2x sin(4 x) 4x 4x e) O y=C, e 4* cos(4 x) + C, e e" sin (2 x) 60 - f) O None of the above.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Give the general solution of the differential equation
4x
p"+4y'+ 20y =2 e** cos( 2x)
1
e** cos( 2x) +
1
e** sin (2 x) + cos( 2 x) C, + C, sin(4 x)
4x
a) O y=
30
4x
60
1
4x
1
4x
b) O y =C, e"cos(2 x) + C, e** sin( 2 x) +
e"cos( 2 x) +
30
e" sin(2x)
60
1
e** cos( 2x)
4x
4x
c) O y=C, e*cos( 2 x) + C, e** sin(2x)
30
60
e" sin(2x)
1
1
e** sin (2 x)
-2x
-2x
4x
4x
d) O y=C, e *cos(4 x) + C, e
+C,e*sin(4x) +
e" cos( 2 x) +
30
60
1
e*"cos( 2 x)
30
-2x
1
-2x
sin(4 x)
4x
4x
e) O y=C, e 4* cos(4 x) + C, e
e" sin (2 x)
60
-
f) O None of the above.
Transcribed Image Text:Give the general solution of the differential equation 4x p"+4y'+ 20y =2 e** cos( 2x) 1 e** cos( 2x) + 1 e** sin (2 x) + cos( 2 x) C, + C, sin(4 x) 4x a) O y= 30 4x 60 1 4x 1 4x b) O y =C, e"cos(2 x) + C, e** sin( 2 x) + e"cos( 2 x) + 30 e" sin(2x) 60 1 e** cos( 2x) 4x 4x c) O y=C, e*cos( 2 x) + C, e** sin(2x) 30 60 e" sin(2x) 1 1 e** sin (2 x) -2x -2x 4x 4x d) O y=C, e *cos(4 x) + C, e +C,e*sin(4x) + e" cos( 2 x) + 30 60 1 e*"cos( 2 x) 30 -2x 1 -2x sin(4 x) 4x 4x e) O y=C, e 4* cos(4 x) + C, e e" sin (2 x) 60 - f) O None of the above.
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