# diff eqn, sin(2x).

• Mar 11th 2009, 12:07 PM
fiksi
diff eqn, sin(2x).
d3y/dx3+dy/dx=sin(2x). Here, i get as far as to lambda is 0,i,-i. Thereafter, I am not sure even how to write this in general form, let alone what to do with that sin thingy... can someone please help?
Also given is: y(0)=1, dy/dx(0)=0, d2y/dx2=0.
• Mar 11th 2009, 12:56 PM
fiksi
Quote:

Originally Posted by fiksi
d3y/dx3+dy/dx=sin(2x). Here, i get as far as to lambda is 0,i,-i. Thereafter, I am not sure even how to write this in general form, let alone what to do with that sin thingy... can someone please help?
Also given is: y(0)=1, dy/dx(0)=0, d2y/dx2=0.

it's not = and =, it was +... corrected it now.
• Mar 12th 2009, 10:30 AM
Coomast
Quote:

Originally Posted by fiksi
d3y/dx3+dy/dx=sin(2x). Here, i get as far as to lambda is 0,i,-i. Thereafter, I am not sure even how to write this in general form, let alone what to do with that sin thingy... can someone please help?
Also given is: y(0)=1, dy/dx(0)=0, d2y/dx2=0.

Hello fiksi,

I assume that you can find the solution for the homogeneous equation, it is:

$y_h=A+B\cdot cos(x)+C\cdot sin(x)$

Now, what you need to use as particular solution is:

$y_p=D\cdot sin(2x)+ E\cdot cos(2x)$

Substitute this in the original DE and it will give you a system for finding D and E. (they are 0 and 1/6)

best regards,

Coomast