![\begin{cases}(D^2+2)x-2y=0\\-2x+(D^2+5)y=0\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%28D%5E2%2B2%29x-2y%3D0%5C%5C-2x%2B%28D%5E2%2B5%29y%3D0%5Cend%7Bcases%7D)
Solve for
in the first ODE:
![y=\dfrac{(D^2+2)x}2](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B%28D%5E2%2B2%29x%7D2)
Substitute this into the second ODE:
![-2x+(D^2+5)\dfrac{(D^2+2)x}2=0](https://tex.z-dn.net/?f=-2x%2B%28D%5E2%2B5%29%5Cdfrac%7B%28D%5E2%2B2%29x%7D2%3D0)
![-4x+(D^4+7D^2+10)x=0](https://tex.z-dn.net/?f=-4x%2B%28D%5E4%2B7D%5E2%2B10%29x%3D0)
![(D^4+7D^2+6)x=0](https://tex.z-dn.net/?f=%28D%5E4%2B7D%5E2%2B6%29x%3D0)
This ODE is linear with characteristic equation
![r^4+7r^2+6=(r^2+6)(r^2+1)=0](https://tex.z-dn.net/?f=r%5E4%2B7r%5E2%2B6%3D%28r%5E2%2B6%29%28r%5E2%2B1%29%3D0)
with roots at
and
, so that the characteristic solution
is
![\boxed{x(t)=C_1\cos(\sqrt6\,t)+C_2\sin(\sqrt6\,t)+C_3\cos t+C_4\sin t}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%28t%29%3DC_1%5Ccos%28%5Csqrt6%5C%2Ct%29%2BC_2%5Csin%28%5Csqrt6%5C%2Ct%29%2BC_3%5Ccos%20t%2BC_4%5Csin%20t%7D)
and from here we can solve for
:
![y=\dfrac{(D^2+2)x}2](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B%28D%5E2%2B2%29x%7D2)
![\boxed{y(t)=-2C_1\cos(\sqrt6\,t)-2C_2\sin(\sqrt6\,t)+\dfrac{C_3}2\cos t+\dfrac{C_4}2\sin t}](https://tex.z-dn.net/?f=%5Cboxed%7By%28t%29%3D-2C_1%5Ccos%28%5Csqrt6%5C%2Ct%29-2C_2%5Csin%28%5Csqrt6%5C%2Ct%29%2B%5Cdfrac%7BC_3%7D2%5Ccos%20t%2B%5Cdfrac%7BC_4%7D2%5Csin%20t%7D)
Answer:
the answer is -0.5.
Step-by-step explanation: First subtract 17 from 15 to know what u need to get. Know that u get -2, we have to figure out what to do to get -2 out of 4. First to get positive 2, multiply by 0.5, than since we need to get negative 2, add a negative in front. Hence, the answer is -0.5 .
Answer:
Step-by-step explanation:
Pace per mile
08 : 59.52
min : sec
Speed
0.1112 miles per minute
=
6.67 miles per hour
Answer:
5.53 seconds.
Step-by-step explanation:
The equation of motion is
d = 4.9t^2 so
150 = .9 t^2
t^2 = 150 / 4.9
t^2 = 30.612
t = 5.53 seconds.
Answer:
Answer is 5
Step-by-step explanation:
When you compare the two you get the following below,
2 to 10
4 to 20
6 to 30
8 to 40
Notice how each mutiplies by 5? Therefore, the answer is 5!