I am using James Stewarts Early Transcendentals Calculus, and Section 9.3 (which is where this problem comes from) doesn't seem to have anything remotely similar to the problem I am facing. No examples, nothing
I hate to just dump a homework problem off, but I really don't know where to begin. I thought "find the tangent line" at first, but it doesn't mention tangent anywhere, and I only thought of that because of previous math classes where I had to find the equation of a tangent line.
Reprinted problem below:
Find an equation of the curve that passes through the point
$(0, 6)$ and whose slope at $(x, y)$ is $\frac{x}{y}$.
Best Answer
The slope at $(x,y)$ is another way of saying the derivative of the curve, so the question can be read as find the equation of a line that satisfies
\begin{equation} \frac{dy}{dx} = \frac{x}{y}, \end{equation}
and that passes through the point $(x,y) = (0,6)$.
Hint: this is a first order ODE that can be solved and will have one constant of integration that can be set such that the solution passes through the desired point.