Happy New Year (2015) | 日本大学吉田研究室 | Yoshida Lab. CIT NIhon University

Jan. 1, 2015

Happy New Year Differential Equation

Norimasa Yoshida (norimasa@acm.org)

Let $w$ be the function of $a$ .The differential equation of $Happy \ New \ Year$ is

(1) $\begin{equation*} \frac{\mathrm{d} w}{\mathrm{d} a} = \frac{1}{a}-r. \end{equation*}$

Integrate Eq.(1) with initial condition of $w(1)=\log \left( \frac{p^{2} h}{n} \right) - r$ , we get

(2) $\begin{eqnarray*} w &=& \int \frac{\mathrm{d} w}{\mathrm{d} a} \mathrm{d} a \\ &=& \log \left( \frac{p^2h}{n} a \right) - r a, \end{eqnarray*}$

where $p, h, n$ are constants and $p \ne 0$ , $h \ne 0$ , $n \ne 0$ .

The graph of Eq.(2) with $p=1,h=1,n=1,r=-1$ is shown below.

Modifying Eq(2),

(3) $\begin{eqnarray*} %w &=& %\log \left( \frac{p^2h}{n} a \right) - r a, \\ \log \left( \frac{p^2h}{n} a \right) &=& w + a r, \\ \frac{p^2h}{n} a &=& e^w e^{r a}, \\ p^2h a y &=& e^w e^{r a} n y, \\ h a p p y &=& n e^w y e^{a r}. \end{eqnarray*}$

References

[1] Solving the Merry Christmas Equation
[2] 数学で「I love you」を伝える方法
[3] ジバニャンの方程式がついに発見される