KneeGrow

03-28-2004, 07:52 PM

Okay here's a few problems that i've solved, i just need some math wiz to check me on my work. Thanks a lot guys, i really appreciate it!

1. y''' - 4y'' + y' + 6y =0

ANSWER: y=(c1)e^(3X) + (c2)e^(2X) + (c3)e^(-X)

2. 4y''' + 28'' + 61y' + 37y =0

ANSWER: y=(c1)e^(-X) + (c2)e^(-3X)(cos0.5X) + (c3)e^(-3X)(sin0.5X)

3.y'''' - 2y''' + 2y'' -2y' + y =0

ANSWER: y=((c1) + c(2)X)e^X + (c3)e^X(cosX) + (c4)e^X(sinX)

4. 4y''''' - 23 y'''' -33y'' - 17y' - 3y =0

ANSWER: y=(c1)e^(3X) + ((c2) + (c3)X)e^(-X) + ((c4) + (c5)X)e^(-0.5X)

FOR # 5/6 I USED METHOD OF UNDETERMINED COEFIFICENTS FOR NONHOMOGENEOUS DIFF EQ'S

5.y'' - 3y' - 4y = 2sinX

ANSWER: y=(c1)e^(4X) + (c2)e^(-X) + (3/17)cosX - (5/17)sinX

6.y'' - 3y' -4y = 4X^2

ANSWER: y= (c1)e^(4X) + (c2)e^(-X) - (1/8) - (1/4)X^2

1. y''' - 4y'' + y' + 6y =0

ANSWER: y=(c1)e^(3X) + (c2)e^(2X) + (c3)e^(-X)

2. 4y''' + 28'' + 61y' + 37y =0

ANSWER: y=(c1)e^(-X) + (c2)e^(-3X)(cos0.5X) + (c3)e^(-3X)(sin0.5X)

3.y'''' - 2y''' + 2y'' -2y' + y =0

ANSWER: y=((c1) + c(2)X)e^X + (c3)e^X(cosX) + (c4)e^X(sinX)

4. 4y''''' - 23 y'''' -33y'' - 17y' - 3y =0

ANSWER: y=(c1)e^(3X) + ((c2) + (c3)X)e^(-X) + ((c4) + (c5)X)e^(-0.5X)

FOR # 5/6 I USED METHOD OF UNDETERMINED COEFIFICENTS FOR NONHOMOGENEOUS DIFF EQ'S

5.y'' - 3y' - 4y = 2sinX

ANSWER: y=(c1)e^(4X) + (c2)e^(-X) + (3/17)cosX - (5/17)sinX

6.y'' - 3y' -4y = 4X^2

ANSWER: y= (c1)e^(4X) + (c2)e^(-X) - (1/8) - (1/4)X^2