## Solution:

The problem of the last contest was:

- 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)`

- 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`

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

### 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:

Name | solutions found | score | chance of winning |
---|---|---|---|

@tonimontana | g(x)=c1*e^x+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.

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

Congratulations @tonimontana, you won 1 SBI:

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

contrabourdon (65)· 11 days agoDifferential equations are scary for normal Steemians...

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tonimontana (57)· 11 days agoYes I think you are right. I also do not like solving differential equations very much.

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