Question

i need another check
\[y'' + 9y = \sec (3t)\]

i got \[y = C_1 \cos (3t) + C_2 \sin (3t) + \cos (3t) \ln |\cos (t)| + \frac{t\sin (3t)}{3}\]

is that right?

Answer 1

ok
first for complementary solution
m^2+9=0
m=+-3i
so
yc=(c1cos(3t)+c2sin(3t)

Answer 2

so complementary is correct:)

Answer 3

now for particular did u use variation of parameters?

Answer 4

wait..i changed my mind...should be 1/9 cos (3t) ln (cos t0

Answer 5

and yes i used variation

Answer 6

ok let me check.
i am just checking not solving :)

Answer 7

uhmm yeah sure

Answer 8

yes you are 100% correct

Answer 9

except for the 1/9 with the log term

Answer 10

it should be 1/9cos(3t)lncos(t)

Answer 11

thanks!!!

Answer 12

yw:)