Solve partialu/dx+dv/dy=0

$$\frac { \partial u } { d x } + \frac { d v } { d y } = 0$$

Solve for u (complex solution)

$$\left\{\begin{matrix}u=0\text{, }&d\neq 0\text{ and }x\neq 0\\u\in \mathrm{C}\text{, }&∂=0\text{ and }d\neq 0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by dx.

$$∂u+dx\frac{\mathrm{d}(v)}{\mathrm{d}y}=0$$

Subtract dx\frac{\mathrm{d}(v)}{\mathrm{d}y} from both sides. Anything subtracted from zero gives its negation.

$$∂u=-dx\frac{\mathrm{d}(v)}{\mathrm{d}y}$$

Reorder the terms.

$$u∂=-dx\frac{\mathrm{d}(v)}{\mathrm{d}y}$$

The equation is in standard form.

$$∂u=0$$

Divide 0 by ∂.

$$u=0$$

Solve for d

$$d\neq 0$$

$$\left(u=0\text{ or }∂=0\right)\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by dx.

$$∂u+dx\frac{\mathrm{d}(v)}{\mathrm{d}y}=0$$

Subtract ∂u from both sides. Anything subtracted from zero gives its negation.

$$dx\frac{\mathrm{d}(v)}{\mathrm{d}y}=-∂u$$

Reorder the terms.

$$dx\frac{\mathrm{d}(v)}{\mathrm{d}y}=-u∂$$

The equation is in standard form.

$$0=-u∂$$

This is false for any d.

$$d\in$$

Solve for u

$$\left\{\begin{matrix}u=0\text{, }&d\neq 0\text{ and }x\neq 0\\u\in \mathrm{R}\text{, }&∂=0\text{ and }d\neq 0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by dx.

$$∂u+dx\frac{\mathrm{d}(v)}{\mathrm{d}y}=0$$

Subtract dx\frac{\mathrm{d}(v)}{\mathrm{d}y} from both sides. Anything subtracted from zero gives its negation.

$$∂u=-dx\frac{\mathrm{d}(v)}{\mathrm{d}y}$$

Reorder the terms.

$$u∂=-dx\frac{\mathrm{d}(v)}{\mathrm{d}y}$$

The equation is in standard form.

$$∂u=0$$

Divide 0 by ∂.

$$u=0$$