Question

Particular solution differential equation at point (8,2), where to go from here?
Problem + work attached

Answer 1

Do you know how to separate variables in a more useful way?

(You are almost surely not going to answer this so I will proceed...)

Answer 2

\[\frac{\text{d}y}{\text{d}x}=\frac{2y}{3x}\]\[\frac{\text{d}y}{y}=2\frac{\text{d}x}{3x}\]\[\int\frac{\text{d}y}{y}=\frac{2}{3}\int\frac{\text{d}x}{x}\]\[\ln (y)=\frac{2}{3}\ln (x)+C\]Does that make sense?

Answer 3

This is supposed to separation of variables, right?

Answer 4

It makes sense to me now, thank you