DE: Inspection for R(x)=sinx or cosx

[median27]

Can you post solved problems using these conditions? We're on the Advanced Engineering Mathematics and reviewing our Differential Equations. My professor only introduces this topic and didn't went deeper. I'm troubled about the sign convention, e.g.:

(D^2-9)y=-sin4x
(D^2-a^2)y=sinbx
yp=-sinbx/(a^2+b^2)
a=3, b=4
yp=sin4x/(3^2+4^2)
yp=sin4x/25

how does yp became positive? What are the formulae used... also for cosine condition?

Thanks for your help!

 

[tiny-tim]

hi median27!

(try using the X² icon just above the Reply box )

I'm troubled about the sign convention …

it's not a convention, it's just the correct formula …

D²(sin4x) = -16sin4x

so (D² - 9)(sin4x) = (-16 - 9)sin4x = -25sin4x

(same for cos4x)

 

[vela]

Your formula tells you the particular solution of

(D²-3²)y = +sin 4x

is
$$y_p = -\frac{\sin 4x}{3^2+4^2}$$
But that's not the differential equation you have. Yours has a negative sign in front of the forcing term, so you must flip the sign of the particular solution.

 

[median27]

can you give me the correct formula to use for sine and cosine?

(D^2-a^2)y=sinbx
yp=-sinbx/(a^2+b^2)... is it the standard formula for sine condition?

 

[tiny-tim]

you can work it out for yourself …

if y = Ksinbx, when will (D² - a²)y equal sinbx ?

 

[median27]

Alright, i get it. Thanks