Solve m(t)=sigmaomega/1+4e^-0,4t

$$m ( t ) = \frac { \sigma \omega } { 1 + 4 e ^ { - 0,4 t } }$$

Solve for m

$$\left\{\begin{matrix}m=\frac{\sigma \omega e^{\frac{2t}{5}}}{t\left(e^{\frac{2t}{5}}+4\right)}\text{, }&t\neq 0\\m\in \mathrm{R}\text{, }&\left(\sigma =0\text{ or }\omega =0\right)\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$tm=\frac{\sigma \omega }{4e^{-\frac{2t}{5}}+1}$$

Divide both sides by t.

$$\frac{tm}{t}=\frac{\sigma \omega e^{\frac{2t}{5}}}{\left(e^{\frac{2t}{5}}+4\right)t}$$

Dividing by t undoes the multiplication by t.

$$m=\frac{\sigma \omega e^{\frac{2t}{5}}}{\left(e^{\frac{2t}{5}}+4\right)t}$$

Divide \frac{\sigma \omega e^{\frac{2t}{5}}}{e^{\frac{2t}{5}}+4} by t.

$$m=\frac{\sigma \omega e^{\frac{2t}{5}}}{t\left(e^{\frac{2t}{5}}+4\right)}$$