integrating by parts

[berryy]

can someone please show me how to solve for q via integrating by parts for:

dq/dt +10q = .25sin5t

i keep getting my constants wrong but when i do it exponetially it works,

Thanks all

[moekamo]

im pretty sure you cant do that with integration by parts...

you can do it though, first find the solution to the homogeneous equation:

- this is seperable, and should be easy ()

then for the particular solution, you take a guess that


finding and subbing back in, then solving for A, B gives the particular solution ()

so the overall, general solution is:

[jimmy999]

You can also do that question using an integration factor. I'm pretty sure by using that method you'll then have to use integration by parts. I won't actually go into it, but a hint, you'll have to use integration by parts twice and collect the common factors

[berryy]

You can also do that question using an integration factor. I'm pretty sure by using that method you'll then have to use integration by parts. I won't actually go into it, but a hint, you'll have to use integration by parts twice and collect the common factors

yeah thats what i meant!
when i integrated it twice, ive stuffed something up when i rearranged the "I" cos my constants are not 1/50 or 1/100

[moekamo]

ahh, ok, in that case , heres what happened when i did it:



which is the same as before, hope this helps find your mistake

[berryy]

i know where i did wrong now
Thankyou heaps for the help