E uchun yechish (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,
E uchun yechish
\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,
Grafik
Baham ko'rish
Klipbordga nusxa olish
y=E-Ec^{\frac{-t}{4}}
E ga 1-c^{\frac{-t}{4}} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
E-Ec^{\frac{-t}{4}}=y
Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.
-Ec^{-\frac{t}{4}}+E=y
Shartlarni qayta saralash.
\left(-c^{-\frac{t}{4}}+1\right)E=y
E'ga ega bo'lgan barcha shartlarni birlashtirish.
\left(1-c^{-\frac{t}{4}}\right)E=y
Tenglama standart shaklda.
\frac{\left(1-c^{-\frac{t}{4}}\right)E}{1-c^{-\frac{t}{4}}}=\frac{y}{1-c^{-\frac{t}{4}}}
Ikki tarafini -c^{-\frac{1}{4}t}+1 ga bo‘ling.
E=\frac{y}{1-c^{-\frac{t}{4}}}
-c^{-\frac{1}{4}t}+1 ga bo'lish -c^{-\frac{1}{4}t}+1 ga ko'paytirishni bekor qiladi.
E=\frac{yc^{\frac{t}{4}}}{c^{\frac{t}{4}}-1}
y ni -c^{-\frac{1}{4}t}+1 ga bo'lish.
y=E-Ec^{\frac{-t}{4}}
E ga 1-c^{\frac{-t}{4}} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
E-Ec^{\frac{-t}{4}}=y
Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.
-Ec^{-\frac{t}{4}}+E=y
Shartlarni qayta saralash.
\left(-c^{-\frac{t}{4}}+1\right)E=y
E'ga ega bo'lgan barcha shartlarni birlashtirish.
\left(1-c^{-\frac{t}{4}}\right)E=y
Tenglama standart shaklda.
\frac{\left(1-c^{-\frac{t}{4}}\right)E}{1-c^{-\frac{t}{4}}}=\frac{y}{1-c^{-\frac{t}{4}}}
Ikki tarafini -c^{-\frac{1}{4}t}+1 ga bo‘ling.
E=\frac{y}{1-c^{-\frac{t}{4}}}
-c^{-\frac{1}{4}t}+1 ga bo'lish -c^{-\frac{1}{4}t}+1 ga ko'paytirishni bekor qiladi.
E=\frac{yc^{\frac{t}{4}}}{c^{\frac{t}{4}}-1}
y ni -c^{-\frac{1}{4}t}+1 ga bo'lish.
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