Math contest #8 Results and Solution

Solution:

The problem of the last contest was:

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 = 1 → k = ±1
   → i(x) = A*e^x + B*e^-x
   → g(x) = x² + 2 + A*e^x + B*e^-x

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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"

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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:

Name	solutions found	score	chance of winning
@tonimontana	g(x)=c1*ex+c2*e(-x)+x^2+2	3	100%

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

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Congratulations @tonimontana, you won 1 SBI:

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