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Differential Equations Sheet #1 - 1st-year Bio Solve the following ODEs:

1-

(D

2

+ 3D + 2 ) y = cos ( 2 x )

2-

(D

3

+ 6 D 2 + 11D + 6 ) y = 2sin ( 3x )

(

)

2 2 2 3- D D + 4 y = 96x

4-

(D

3

− 7 D + 6 ) y = x 3e 2 x

5-

(D

2

− 6 D + 13) y = 8e 3x sin(2x )

6-

(x

D 3 + 3x 2 D 2 + xD ) y = 24x 2

7-

(D

2

− 5D + 6 ) y = 2e 3x − 3e −2 x + 12

8-

(D

3

+ 4 D 2 + 3D ) y = x 2

9-

(D

3

+ D2) y = x 2 −x +2

3

(

)

2 x 2 10- D − 2 D + 1 y = e (1 + 2x + 3x )

(

)

2 11- D + D + 1 y = sin ( 2x

(

)

)

2 12- D + 4 y = 2sin( x ) + cos(2 x )

(

)

2 2 2x 13- D − 4 D + 4 y = sin ( 2 x ) + x + e

(

)

2 2 4 14- x D + 6xD + 6 y = x

(

)

3 3 2 2 2 15- x D + 5x D + 3xD y = x

(

)

5 4 3 16- D − D − D + 1 y = 6x − 3x − 9

(

)

2 2 17- D + 4 y = 4sin ( x )

(

)

4 2 18- D + 10D + 9 y = cos(2 x )


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1st Year Bio Mathematics Sheet 1  

1st Year Bio Mathematics Sheet 1

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