Whakaoti mō E (complex solution)
\left\{\begin{matrix}E=-\frac{yc^{\frac{t}{4}}}{1-c^{\frac{t}{4}}}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }c=e^{-\frac{\pi n_{1}iRe(t)}{2\times \frac{\left(Re(t)\right)^{2}+\left(Im(t)\right)^{2}}{16}}-\frac{\pi n_{1}Im(t)}{2\times \frac{\left(Re(t)\right)^{2}+\left(Im(t)\right)^{2}}{16}}}\\E\in \mathrm{C}\text{, }&\left(c=0\text{ and }t\neq 0\right)\text{ or }\left(y=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }c=e^{-\frac{\pi n_{1}iRe(t)}{2\times \frac{\left(Re(t)\right)^{2}+\left(Im(t)\right)^{2}}{16}}-\frac{\pi n_{1}Im(t)}{2\times \frac{\left(Re(t)\right)^{2}+\left(Im(t)\right)^{2}}{16}}}\right)\end{matrix}\right.
Whakaoti mō E
\left\{\begin{matrix}E=-\frac{yc^{\frac{t}{4}}}{1-c^{\frac{t}{4}}}\text{, }&\left(t\neq 0\text{ and }c\neq -1\text{ and }Denominator(\frac{t}{4})\text{bmod}2=1\text{ and }c<0\text{ and }Denominator(-\frac{t}{4})\text{bmod}2=1\right)\text{ or }\left(c<0\text{ and }Numerator(\frac{t}{4})\text{bmod}2=1\text{ and }Denominator(\frac{t}{4})\text{bmod}2=1\text{ and }Denominator(-\frac{t}{4})\text{bmod}2=1\right)\text{ or }\left(t\neq 0\text{ and }c\neq 1\text{ and }c>0\right)\\E\in \mathrm{R}\text{, }&\left(y=0\text{ and }t=0\text{ and }c\neq 0\right)\text{ or }\left(Numerator(\frac{t}{4})\text{bmod}2=0\text{ and }y=0\text{ and }Denominator(\frac{t}{4})\text{bmod}2=1\text{ and }Denominator(-\frac{t}{4})\text{bmod}2=1\text{ and }c=-1\right)\text{ or }\left(c=1\text{ and }y=0\right)\text{ or }\left(c=0\text{ and }t<0\right)\end{matrix}\right.
Graph
Tohaina
Kua tāruatia ki te papatopenga
y=E-Ec^{\frac{-t}{4}}
Whakamahia te āhuatanga tohatoha hei whakarea te E ki te 1-c^{\frac{-t}{4}}.
E-Ec^{\frac{-t}{4}}=y
Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.
-Ec^{-\frac{t}{4}}+E=y
Whakaraupapatia anō ngā kīanga tau.
\left(-c^{-\frac{t}{4}}+1\right)E=y
Pahekotia ngā kīanga tau katoa e whai ana i te E.
\left(1-c^{-\frac{t}{4}}\right)E=y
He hanga arowhānui tō te whārite.
\frac{\left(1-c^{-\frac{t}{4}}\right)E}{1-c^{-\frac{t}{4}}}=\frac{y}{1-c^{-\frac{t}{4}}}
Whakawehea ngā taha e rua ki te -c^{-\frac{1}{4}t}+1.
E=\frac{y}{1-c^{-\frac{t}{4}}}
Mā te whakawehe ki te -c^{-\frac{1}{4}t}+1 ka wetekia te whakareanga ki te -c^{-\frac{1}{4}t}+1.
E=\frac{yc^{\frac{t}{4}}}{c^{\frac{t}{4}}-1}
Whakawehe y ki te -c^{-\frac{1}{4}t}+1.
y=E-Ec^{\frac{-t}{4}}
Whakamahia te āhuatanga tohatoha hei whakarea te E ki te 1-c^{\frac{-t}{4}}.
E-Ec^{\frac{-t}{4}}=y
Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.
-Ec^{-\frac{t}{4}}+E=y
Whakaraupapatia anō ngā kīanga tau.
\left(-c^{-\frac{t}{4}}+1\right)E=y
Pahekotia ngā kīanga tau katoa e whai ana i te E.
\left(1-c^{-\frac{t}{4}}\right)E=y
He hanga arowhānui tō te whārite.
\frac{\left(1-c^{-\frac{t}{4}}\right)E}{1-c^{-\frac{t}{4}}}=\frac{y}{1-c^{-\frac{t}{4}}}
Whakawehea ngā taha e rua ki te -c^{-\frac{1}{4}t}+1.
E=\frac{y}{1-c^{-\frac{t}{4}}}
Mā te whakawehe ki te -c^{-\frac{1}{4}t}+1 ka wetekia te whakareanga ki te -c^{-\frac{1}{4}t}+1.
E=\frac{yc^{\frac{t}{4}}}{c^{\frac{t}{4}}-1}
Whakawehe y ki te -c^{-\frac{1}{4}t}+1.
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