ME 526: ENGINEERING ANALYTICAL METHODS

Homework #1

Due, Tuesday June 1, 1999

Obtain the general solutions of the following homogeneous differential equations:

1. y'' + 13y' + 40y = 0 2. y'' + 2y' -15y = 0 3. y'' + 2y' +5y = 0

4. y''' - 7y' + 6y = 0 5. y''' -5y'' + 9y' =0

 

Find the general solution for the following non-homogeneous differential equations by the method of undetermined coefficients:

1. y'' + 2y' + y = e-2x 2. y'' + y' -12y = sin2x

3. y'' - 7y' + 6y = sinx+2cos3x 4. y'' - 2y' + 10y = ex cos3x

5. y'' - 9y' + 14y = x2 + 4x 6. y'' + 9y = x3 + xcos3x

 

Solve the following equations by the method of Variation of Parameters:

1. y'' - 2y' + y = ex/x2 2. y'' - y = 1/sinhx

3. y'' + 4y' + 8y = 2e-2x tan2x 4. y'' - 6y' + 9y = xe-3x lnx