Solve dx+e^3xdv=0

$$d x + e ^ { 3 x } d v = 0$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&v=-\frac{x}{e^{3x}}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing d.

$$\left(x+e^{3x}v\right)d=0$$

The equation is in standard form.

$$\left(x+ve^{3x}\right)d=0$$

Divide 0 by x+e^{3x}v.

$$d=0$$

Solve for v (complex solution)

$$\left\{\begin{matrix}\\v=-\frac{x}{e^{3x}}\text{, }&\text{unconditionally}\\v\in \mathrm{C}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract dx from both sides. Anything subtracted from zero gives its negation.

$$e^{3x}dv=-dx$$

Reorder the terms.

$$dve^{3x}=-dx$$

The equation is in standard form.

$$de^{3x}v=-dx$$

Divide both sides by e^{3x}d.

$$\frac{de^{3x}v}{de^{3x}}=-\frac{dx}{de^{3x}}$$

Dividing by e^{3x}d undoes the multiplication by e^{3x}d.

$$v=-\frac{dx}{de^{3x}}$$

Divide -dx by e^{3x}d.

$$v=-\frac{x}{e^{3x}}$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&v=-\frac{x}{e^{3x}}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing d.

$$\left(x+e^{3x}v\right)d=0$$

The equation is in standard form.

$$\left(x+ve^{3x}\right)d=0$$

Divide 0 by x+e^{3x}v.

$$d=0$$

Solve for v

$$\left\{\begin{matrix}\\v=-\frac{x}{e^{3x}}\text{, }&\text{unconditionally}\\v\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract dx from both sides. Anything subtracted from zero gives its negation.

$$e^{3x}dv=-dx$$

Reorder the terms.

$$dve^{3x}=-dx$$

The equation is in standard form.

$$de^{3x}v=-dx$$

Divide both sides by e^{3x}d.

$$\frac{de^{3x}v}{de^{3x}}=-\frac{dx}{de^{3x}}$$

Dividing by e^{3x}d undoes the multiplication by e^{3x}d.

$$v=-\frac{dx}{de^{3x}}$$

Divide -dx by e^{3x}d.

$$v=-\frac{x}{e^{3x}}$$