\frac { d y } { \sqrt { e ^ { 2 y } - 1 } } = \pm d x
Solve for x
\left\{\begin{matrix}x=\frac{dy}{\sqrt{e^{2y}-1}\left(±d\right)}\text{, }&±d\neq 0\text{ and }y>0\\x\in \mathrm{R}\text{, }&d=0\text{ and }y>0\end{matrix}\right.
Share
Copied to clipboard
\left(±d\right)x=\frac{dy}{\sqrt{e^{2y}-1}}
Swap sides so that all variable terms are on the left hand side.
\frac{\left(±d\right)x}{±d}=\frac{dy}{\sqrt{e^{2y}-1}\left(±d\right)}
Divide both sides by ±d.
x=\frac{dy}{\sqrt{e^{2y}-1}\left(±d\right)}
Dividing by ±d undoes the multiplication by ±d.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\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]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}