Datrys ar gyfer 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.
Datrys ar gyfer 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.
Graff
Rhannu
Copïo i clipfwrdd
y=E-Ec^{\frac{-t}{4}}
Defnyddio’r briodwedd ddosbarthu i luosi E â 1-c^{\frac{-t}{4}}.
E-Ec^{\frac{-t}{4}}=y
Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.
-Ec^{-\frac{t}{4}}+E=y
Aildrefnu'r termau.
\left(-c^{-\frac{t}{4}}+1\right)E=y
Cyfuno pob term sy'n cynnwys E.
\left(1-c^{-\frac{t}{4}}\right)E=y
Mae'r hafaliad yn y ffurf safonol.
\frac{\left(1-c^{-\frac{t}{4}}\right)E}{1-c^{-\frac{t}{4}}}=\frac{y}{1-c^{-\frac{t}{4}}}
Rhannu’r ddwy ochr â -c^{-\frac{1}{4}t}+1.
E=\frac{y}{1-c^{-\frac{t}{4}}}
Mae rhannu â -c^{-\frac{1}{4}t}+1 yn dad-wneud lluosi â -c^{-\frac{1}{4}t}+1.
E=\frac{yc^{\frac{t}{4}}}{c^{\frac{t}{4}}-1}
Rhannwch y â -c^{-\frac{1}{4}t}+1.
y=E-Ec^{\frac{-t}{4}}
Defnyddio’r briodwedd ddosbarthu i luosi E â 1-c^{\frac{-t}{4}}.
E-Ec^{\frac{-t}{4}}=y
Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.
-Ec^{-\frac{t}{4}}+E=y
Aildrefnu'r termau.
\left(-c^{-\frac{t}{4}}+1\right)E=y
Cyfuno pob term sy'n cynnwys E.
\left(1-c^{-\frac{t}{4}}\right)E=y
Mae'r hafaliad yn y ffurf safonol.
\frac{\left(1-c^{-\frac{t}{4}}\right)E}{1-c^{-\frac{t}{4}}}=\frac{y}{1-c^{-\frac{t}{4}}}
Rhannu’r ddwy ochr â -c^{-\frac{1}{4}t}+1.
E=\frac{y}{1-c^{-\frac{t}{4}}}
Mae rhannu â -c^{-\frac{1}{4}t}+1 yn dad-wneud lluosi â -c^{-\frac{1}{4}t}+1.
E=\frac{yc^{\frac{t}{4}}}{c^{\frac{t}{4}}-1}
Rhannwch y â -c^{-\frac{1}{4}t}+1.
Enghreifftiau
Hafaliad cwadratig
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometreg
4 \sin \theta \cos \theta = 2 \sin \theta
Hafaliad llinol
y = 3x + 4
Rhifyddeg
699 * 533
Matrics
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Hafaliad ar y pryd
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Gwahaniaethu
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integreiddiad
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Terfynau
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}