Question

The integral curves of $\frac {dx}{a} = \frac {dy}{b} = dz$ is

Answer 1

Let's consider $\frac{dx}{a}= \frac{dy}{b}.$ Antiderivatives are related by the folowing equalitie $\frac{x}{a}=\frac{y}{b}+c_1$ .

Let's consider the $\frac{dx}{a}= dz$ . Antiderivatives are related by the folowing equalitie $\frac{x}{a}=z+c_2.$

So the answer is $\frac{x}{a}=\frac{y+c_1b}{b}=z+c_2$