Suppose 
is another solution. Then
Substituting these derivatives into the ODE gives
Let 
, so that
Then the ODE becomes
and we can condense the left hand side as a derivative of a product,
![\dfrac{\mathrm d}{\mathrm dx}[x^5u]=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5E5u%5D%3D0)
Integrate both sides with respect to 
:
![\displaystyle\int\frac{\mathrm d}{\mathrm dx}[x^5u]\,\mathrm dx=C](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5E5u%5D%5C%2C%5Cmathrm%20dx%3DC)
Solve for 
:
Solve for 
:
So another linearly independent solution is 
.
You didn't include the formula.
Given that there is no data about the mass, I will suppose that the formula is that of the simple pendulum (which is only valid if the mass is negligible).
Any way my idea is to teach you how to use the formula and you can apply the procedure to the real formula that the problem incorporates.
Simple pendulum formula:
Period = 2π √(L/g)
Square both sides
Period^2 = (2π)^2 L/g
L = [Period / 2π)^2 * g
Period = 3.1 s
2π ≈ 6.28
g ≈ 10 m/s^2
L = [3.1s/6.28]^2 * 10m/s^2 =2.43 m
I hope this helps you.
Answer:
x=10
Step-by-step explanation:
13x-7+7x-13=180
Combine like terms
20x-20 = 180
Add 20 to each side
20x -20+20 = 180+20
20x=200
Divide by 20
20x/20 = 200/20
x = 10
You should add the two bases and muliply them with the height and then divide with 2
(14+18)×10÷2=160
1) So the ratio of Machine A to B is x + 16 : x (x being the paper printed in machine b).
2) This is in 4 minutes so every minute it will be 152.
2) So x + 16 + x = 152, or 2x + 16 = 152.
3) So to find x, we can subtract 16 from both sides. 2x = 136
4) Now we just divide both sides by 2 to get x = 68.
5) So machine A will be 68 + 16 = 84.
= 84
⭐ Answered by Foxzy0⭐
⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
