Solve d/dty-ae^-kt=-{k}_{1}y

$$\frac{d}{d t } y -a { e }^{ -kt } = - { k }_{ 1 } y$$

Solve for a

$$a=ke^{kt}$$

Steps for Solving Linear Equation

Subtract \frac{\mathrm{d}}{\mathrm{d}t}(y) from both sides.

$$-ae^{-kt}=-k-\frac{\mathrm{d}}{\mathrm{d}t}(y)$$

The equation is in standard form.

$$\left(-\frac{1}{e^{kt}}\right)a=-k$$

Divide both sides by -e^{-kt}.

$$\frac{\left(-\frac{1}{e^{kt}}\right)a}{-\frac{1}{e^{kt}}}=-\frac{k}{-\frac{1}{e^{kt}}}$$

Dividing by -e^{-kt} undoes the multiplication by -e^{-kt}.

$$a=-\frac{k}{-\frac{1}{e^{kt}}}$$

Divide -k by -e^{-kt}.

$$a=ke^{kt}$$