Thread: differential equations 2

just thought that i would post the last 4 differential equations because these are the last 4 i dont know how to do

1) (d2y/dx2)-3(dy/dx)+2y=0

2) (d2y/dx2)-3(dy/dx)+2y=e^5x

3) (d2y/dx2)-3(dy/dx)+2y=e^x

they all work on eachother so shouldnt be that hard...right?!

Originally Posted by emily28

1) (d2y/dx2)-3(dy/dx)+2y=0

Thus,

2) (d2y/dx2)-3(dy/dx)+2y=e^5x

Look for particular of form,

3) (d2y/dx2)-3(dy/dx)+2y=e^x

Look for particular of form,

4) (d2y/dx2)-3(dy/dx)+2y=xe^2x

Look for particular of form,

Quote:
2) (d2y/dx2)-3(dy/dx)+2y=e^5x
Look for particular of form,


i have used the particular solution of

so


and

which is

then -3 +2Cxe^{5x} = e^{5x}

giving 10c - 3c = 1
and c=1/7

so the general solution is


is this right?

Quote:
3) (d2y/dx2)-3(dy/dx)+2y=e^x
Look for particular of form,



i have used the particular solution of

so


and

which is

then -3 +2Cxe^{x} = e^{x}

giving 2c - 3c = 1
and c=-1

so the general solution is


is this right?

are my previous attempts right and does anyone know where i have gone wrong on the last attempt? any advice would be appreciated

please could someone tell me if ive got the previous attempts right? it would really help

Originally Posted by emily28

Quote:
2) (d2y/dx2)-3(dy/dx)+2y=e^5x
Look for particular of form,


i have used the particular solution of

so


and

which is

then -3 +2Cxe^{5x} = e^{5x}

giving 10c - 3c = 1
and c=1/7

so the general solution is


is this right?

this solution is not correct. why didn't you use as suggested?

Originally Posted by emily28

Quote:
3) (d2y/dx2)-3(dy/dx)+2y=e^x
Look for particular of form,



i have used the particular solution of

so


and

which is

then -3 +2Cxe^{x} = e^{x}

giving 2c - 3c = 1
and c=-1

so the general solution is


is this right?

this solution is correct.

good job

cheers its good to know one of them was right, ill have another attempt at 2) and Jhevon do you know if what i have done of my final one is correct?

looking at

2) (d2y/dx2)-3(dy/dx)+2y=e^5x
Look for particular of form,




and

then

giving 12c = 1
and c=1/12

so the general solution is


is this right now ?

Originally Posted by emily28

looking at

2) (d2y/dx2)-3(dy/dx)+2y=e^5x
Look for particular of form,




and

then

giving 12c = 1
and c=1/12

so the general solution is


is this right now ?

Look right to me.