Solve dθ/dx+dz/dθ=phidθ

$$\frac { d \theta } { d x } + \frac { d z } { d \theta } = \phi d \theta$$

Solve for d (complex solution)

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&\theta =0\text{ or }ϕ=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ϕd\theta =\frac{\mathrm{d}(\theta )}{\mathrm{d}x}+\frac{\mathrm{d}(z)}{\mathrm{d}\theta }$$

The equation is in standard form.

$$\theta ϕd=0$$

Divide 0 by ϕ\theta .

$$d=0$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&\theta =0\text{ or }ϕ=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ϕd\theta =\frac{\mathrm{d}(\theta )}{\mathrm{d}x}+\frac{\mathrm{d}(z)}{\mathrm{d}\theta }$$

The equation is in standard form.

$$\theta ϕd=0$$

Divide 0 by ϕ\theta .

$$d=0$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

$$\theta =0\text{ or }d=0\text{ or }ϕ=0$$

Solve for x

$$x\in \mathrm{R}$$

$$\theta =0\text{ or }d=0\text{ or }ϕ=0$$