Solve for c (complex solution)
c=\frac{\sqrt{y^{2}-1}+y}{e^{x}}
Solve for c
c=\frac{\sqrt{y^{2}-1}+y}{e^{x}}
|y|\geq 1
Solve for x (complex solution)
x=2\pi n_{1}i+\ln(\frac{\sqrt{y^{2}-1}+y}{c})
n_{1}\in \mathrm{Z}
c\neq 0
Solve for x
x=\ln(\frac{\sqrt{y^{2}-1}+y}{c})
\left(c<0\text{ and }y\leq -1\right)\text{ or }\left(c>0\text{ and }y\geq 1\right)
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ce^{x}=y+\sqrt{y^{2}-1}
Swap sides so that all variable terms are on the left hand side.
e^{x}c=\sqrt{y^{2}-1}+y
The equation is in standard form.
\frac{e^{x}c}{e^{x}}=\frac{\sqrt{y^{2}-1}+y}{e^{x}}
Divide both sides by e^{x}.
c=\frac{\sqrt{y^{2}-1}+y}{e^{x}}
Dividing by e^{x} undoes the multiplication by e^{x}.
ce^{x}=y+\sqrt{y^{2}-1}
Swap sides so that all variable terms are on the left hand side.
e^{x}c=\sqrt{y^{2}-1}+y
The equation is in standard form.
\frac{e^{x}c}{e^{x}}=\frac{\sqrt{y^{2}-1}+y}{e^{x}}
Divide both sides by e^{x}.
c=\frac{\sqrt{y^{2}-1}+y}{e^{x}}
Dividing by e^{x} undoes the multiplication by e^{x}.
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