Answer to Question #238845 in Differential Equations for vish

Question

The integral curves of dx/a = dy/b = dz is

Answer 1

Let us find the integral curves of $\frac{dx}{a} = \frac{dy}{b} = dz.$ It is equivalent to $dz=\frac{dx}{a}$ and $dz= \frac{dy}{b}.$ Then$\int dz=\int\frac{dx}{a}$ and $\int dz= \int\frac{dy}{b}.$ It follows that $z=\frac{x}{a} +C_1$ and $z= \frac{y}{b}+C_2.$ Therefore, $z=\frac{x}{a} +C_1=\frac{y}{b}+C_2$ is the required integral curves.