Question

Verify that the general solution satisfies the differential equation. Then find the particular solution that satisfies the initial condition.
y = C1 sin(3x) + C2 cos(3x)
y'' + 9y = 0
y = 7 when x = π/6
y' = 10 when x = π/6

Answer 1

Hi do you have any problem in the first part ?

Answer 2

No, what I'm missing & don't know how to find is C1 & C2

Answer 3

show me the solution how far you reached

Answer 4

i have 7 = C1 sin pi/6 + C2 cos pi/6
then 10 = C1 sin pi/6 + C2 cos pi/6

Answer 5

its not pi/6.. it will be pi/2

Answer 6

why

Answer 7

3x=3pi/6=pi/2

Answer 8

OH okay well I'm still unsure on how to solve

Answer 9

Well you need to solve as follows

Answer 10

see you made another mistake

Answer 11

what would that be

Answer 12

y = C1 sin(3x) + C2 cos(3x) gives y'=3C1 cos(3x)-3C2sin(3x)
and so 10=3C1 cos pi/2 -3C2 si pi/2

Answer 13

so we have the equations 7 = C1 sin pi/2 + C2 cos pi/2 =C1
and 10=-3C2 since sin pi/2=1 and cos pi/2=0
hence we have C1=7 and C2=-10/3

Answer 14

@shelby.lane did you get the solution?

Answer 15

I'm checking over it now

Answer 16

yes! thank you!

Answer 17

np.:)