Issolvi y=E(1-c^-t/4)

$$y = E ( 1 - c ^ { - t / 4 } )$$

Solvi għal E (complex solution)

$$\left\{\begin{matrix}E=-\frac{yc^{\frac{t}{4}}}{1-c^{\frac{t}{4}}}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }c=e^{-\frac{\pi n_{1}iRe(t)}{2\times \frac{\left(Re(t)\right)^{2}+\left(Im(t)\right)^{2}}{16}}-\frac{\pi n_{1}Im(t)}{2\times \frac{\left(Re(t)\right)^{2}+\left(Im(t)\right)^{2}}{16}}}\\E\in \mathrm{C}\text{, }&\left(c=0\text{ and }t\neq 0\right)\text{ or }\left(y=0\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }c=e^{-\frac{\pi n_{1}iRe(t)}{2\times \frac{\left(Re(t)\right)^{2}+\left(Im(t)\right)^{2}}{16}}-\frac{\pi n_{1}Im(t)}{2\times \frac{\left(Re(t)\right)^{2}+\left(Im(t)\right)^{2}}{16}}}\right)\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika E b'1-c^{\frac{-t}{4}}.

$$y=E-Ec^{\frac{-t}{4}}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$E-Ec^{\frac{-t}{4}}=y$$

Erġa' ordna t-termini.

$$-Ec^{-\frac{t}{4}}+E=y$$

Ikkombina t-termini kollha li fihom E.

$$\left(-c^{-\frac{t}{4}}+1\right)E=y$$

L-ekwazzjoni hija f'forma standard.

$$\left(1-c^{-\frac{t}{4}}\right)E=y$$

Iddividi ż-żewġ naħat b'-c^{-\frac{1}{4}t}+1.

$$\frac{\left(1-c^{-\frac{t}{4}}\right)E}{1-c^{-\frac{t}{4}}}=\frac{y}{1-c^{-\frac{t}{4}}}$$

Meta tiddividi b'-c^{-\frac{1}{4}t}+1 titneħħa l-multiplikazzjoni b'-c^{-\frac{1}{4}t}+1.

$$E=\frac{y}{1-c^{-\frac{t}{4}}}$$

Iddividi y b'-c^{-\frac{1}{4}t}+1.

$$E=\frac{yc^{\frac{t}{4}}}{c^{\frac{t}{4}}-1}$$

Solvi għal E

$$\left\{\begin{matrix}E=-\frac{yc^{\frac{t}{4}}}{1-c^{\frac{t}{4}}}\text{, }&\left(t\neq 0\text{ and }c\neq -1\text{ and }Denominator(\frac{t}{4})\text{bmod}2=1\text{ and }c<0\text{ and }Denominator(-\frac{t}{4})\text{bmod}2=1\right)\text{ or }\left(c<0\text{ and }Numerator(\frac{t}{4})\text{bmod}2=1\text{ and }Denominator(\frac{t}{4})\text{bmod}2=1\text{ and }Denominator(-\frac{t}{4})\text{bmod}2=1\right)\text{ or }\left(t\neq 0\text{ and }c\neq 1\text{ and }c>0\right)\\E\in \mathrm{R}\text{, }&\left(y=0\text{ and }t=0\text{ and }c\neq 0\right)\text{ or }\left(Numerator(\frac{t}{4})\text{bmod}2=0\text{ and }y=0\text{ and }Denominator(\frac{t}{4})\text{bmod}2=1\text{ and }Denominator(-\frac{t}{4})\text{bmod}2=1\text{ and }c=-1\right)\text{ or }\left(c=1\text{ and }y=0\right)\text{ or }\left(c=0\text{ and }t<0\right)\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika E b'1-c^{\frac{-t}{4}}.

$$y=E-Ec^{\frac{-t}{4}}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$E-Ec^{\frac{-t}{4}}=y$$

Erġa' ordna t-termini.

$$-Ec^{-\frac{t}{4}}+E=y$$

Ikkombina t-termini kollha li fihom E.

$$\left(-c^{-\frac{t}{4}}+1\right)E=y$$

L-ekwazzjoni hija f'forma standard.

$$\left(1-c^{-\frac{t}{4}}\right)E=y$$

Iddividi ż-żewġ naħat b'-c^{-\frac{1}{4}t}+1.

$$\frac{\left(1-c^{-\frac{t}{4}}\right)E}{1-c^{-\frac{t}{4}}}=\frac{y}{1-c^{-\frac{t}{4}}}$$

Meta tiddividi b'-c^{-\frac{1}{4}t}+1 titneħħa l-multiplikazzjoni b'-c^{-\frac{1}{4}t}+1.

$$E=\frac{y}{1-c^{-\frac{t}{4}}}$$

Iddividi y b'-c^{-\frac{1}{4}t}+1.

$$E=\frac{yc^{\frac{t}{4}}}{c^{\frac{t}{4}}-1}$$