Solve Pe^3t-Qe^-4t=0

$$P e ^ { 3 t } - Q e ^ { - 4 t } = 0$$

Solve for P

$$P=\frac{Q}{e^{7t}}$$

Steps for Solving Linear Equation

Add Qe^{-4t} to both sides.

$$Pe^{3t}=0+Qe^{-4t}$$

Anything plus zero gives itself.

$$Pe^{3t}=Qe^{-4t}$$

The equation is in standard form.

$$e^{3t}P=\frac{Q}{e^{4t}}$$

Divide both sides by e^{3t}.

$$\frac{e^{3t}P}{e^{3t}}=\frac{Q}{e^{4t}e^{3t}}$$

Dividing by e^{3t} undoes the multiplication by e^{3t}.

$$P=\frac{Q}{e^{4t}e^{3t}}$$

Divide \frac{Q}{e^{4t}} by e^{3t}.

$$P=\frac{Q}{e^{7t}}$$

Solve for Q

$$Q=Pe^{7t}$$

Steps for Solving Linear Equation

Subtract Pe^{3t} from both sides. Anything subtracted from zero gives its negation.

$$-Qe^{-4t}=-Pe^{3t}$$

The equation is in standard form.

$$\left(-\frac{1}{e^{4t}}\right)Q=-Pe^{3t}$$

Divide both sides by -e^{-4t}.

$$\frac{\left(-\frac{1}{e^{4t}}\right)Q}{-\frac{1}{e^{4t}}}=-\frac{Pe^{3t}}{-\frac{1}{e^{4t}}}$$

Dividing by -e^{-4t} undoes the multiplication by -e^{-4t}.

$$Q=-\frac{Pe^{3t}}{-\frac{1}{e^{4t}}}$$

Divide -Pe^{3t} by -e^{-4t}.

$$Q=Pe^{7t}$$