Answer:
general solution=
+5
Step-by-step explanation:
using linear differential equation method
y'' + y' + y = 5
writing down the characteristics equation.
![m^2+m+1=0](https://tex.z-dn.net/?f=m%5E2%2Bm%2B1%3D0)
using quadratic formula
![m=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
we get
![m=\frac{-1\pm \sqrt{1^2-4(1)(1)}}{2(1)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1%5Cpm%20%5Csqrt%7B1%5E2-4%281%29%281%29%7D%7D%7B2%281%29%7D)
![m=-\frac{1}{2} \pm \frac{3}{2} i](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B1%7D%7B2%7D%20%5Cpm%20%5Cfrac%7B3%7D%7B2%7D%20i)
now Complementary function(CF)
![y=e^{ax}(Acosbx+Bsinbx)\\y=e^{-\frac{1}{2} x}(Acos\frac{3}{2} x+Bsin\frac{3}{2}x)](https://tex.z-dn.net/?f=y%3De%5E%7Bax%7D%28Acosbx%2BBsinbx%29%5C%5Cy%3De%5E%7B-%5Cfrac%7B1%7D%7B2%7D%20x%7D%28Acos%5Cfrac%7B3%7D%7B2%7D%20x%2BBsin%5Cfrac%7B3%7D%7B2%7Dx%29)
now for particular integrals
![D^2y+Dy+y=5\\(D^2+D+1)y=5\\y=\frac{5}{D^2+D+1}](https://tex.z-dn.net/?f=D%5E2y%2BDy%2By%3D5%5C%5C%28D%5E2%2BD%2B1%29y%3D5%5C%5Cy%3D%5Cfrac%7B5%7D%7BD%5E2%2BD%2B1%7D)
![P.I.=\frac{5\times e^{0x} }{D^2+D+1}](https://tex.z-dn.net/?f=P.I.%3D%5Cfrac%7B5%5Ctimes%20e%5E%7B0x%7D%20%7D%7BD%5E2%2BD%2B1%7D)
putting D=0
we get
P.I.=5
general solution=CF+PI
general solution=
+5
Answer: Its the third one from up. Second from bottom.
Step-by-step explanation: I looked at all of the other ones and they did not make sense. Let me know if I got wrong. God Bless!
12,000 people voted.
90,000/7.5=12,000
Answer:
Haeather ran at a speed of 5 miles per hour.
Step-by-step explanation:
Given that last week at the park Haeather ran 4 miles in 48 minutes, to determine what was Haeather rate of speed in miles per hour the following mathematical calculation must be performed:
48/4 = 12
Thus, Haeather ran 1 mile every 12 minutes.
60/12 = 5
1 x 5 = 5
Therefore, Haeather ran at a speed of 5 miles per hour.
You need to write this question out in algebra form first. X + x + 1 + x + 2 = 72 than you add the like terms
3x + 3 = 72 ... 3x=69 ... x=69/3 ... x=23. So we have now found x now you just add 1 to x and get 24 and you add 2 to x you will get 25.
Add 23 + 24 + 25 together you will get 72