Math contest #8 Results and Solution

in #puzzlelast year

Solution:

The problem of the last contest was:
Screenshot from 2019-09-03 10-01-47.png

  1. solution:
    f(x) = df(x)/dx |×dx ÷f(x)
    dx = 1/f(x) × df(x) |integrate
    x + C = ln(f(x)) |e^()
    f(x) = e^(x+C)
  2. solution:
    Assumption: g(x) = x²+h(x)
    g''(x) = h''(x) + (x²)'' = h''(x) + 2
    h(x) = h''(x) + 2
    h(x) = i(x)+2
    i(x) = i''(x)
    Assumption: i(x) = e^(kx)
    e^(kx) = k²*e^(kx)
    k² = 1k = ±1
    i(x) = A*e^x + B*e^-x
    g(x) = x² + 2 + A*e^x + B*e^-x

↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

How your chance of winning is calculated:

  • Every participant gets 1 point for entering the contest.
  • Every solution entered gets 1 additional point.
  • Multiple examples of a general solution count as one solution
  • If there is only one general solution, those who found its pattern(by mentioning a general formula or showing more then 3 examples) will get an additional point.
  • Your winning chance is "your points"/"total points"

↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓
All participants did great and got the maximum score, but I list the score anyway.

List of participants with their scores and chance of winning, sorted by time of entry:

Namesolutions foundscorechance of winning
@tonimontanag(x)=c1*e^x+c2*e^(-x)+x^2+23100%

Judging by the participants it seems like differential equation is not a thing for this contest. So I'll go back to normal equation.

↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓
Congratulations @tonimontana, you won 1 SBI:
Screenshot from 2019-09-05 11-18-05.png
↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

The next contest starts tomorrow. Don't miss it!

Sort:  

Differential equations are scary for normal Steemians...

Yes I think you are right. I also do not like solving differential equations very much.