Determine if linear or non-linear, homogeneous or nonhomogeneous, with constant or variable coefficients.

Determine if linearly dependent or linearly independent.

a.

b.

c.

d.

NOTE:

If the root λ is repeated k time, the solution corresponding to this is

xλ1kk21 e)xc...xcc(y

If the pair of roots λ1,2 = a ± bi is a complex, conjugate pair, the solution corresponding to this is

)bxsincbxcosc(ey 21ax

General Solution of the Homogeneous, Linear ODE with Constant Coefficients

The general solution of the homogeneous linear ODE with constant coefficients is the linear combination of the above solutions.

1.

2.

3.

4.

Find the general solution of the following

0y)2D3D2D2D( 235

0y)1D2D4D8( 23

0y)4D8D5D2D( 234

1.

2.

3.

ASSIGNMENT

Solve by method of undetermined coefficients.

1.

2.

3.

4.

Solve by variation of parameters1.

2.

3.