Mathematics

Problem

A function

y=y(x)

satisfies the differential equation

\frac{dy}{dx}=\frac{3y}{x}, \quad x>0,

and the initial condition

y(2)=5

. a. Determine the general solution in explicit form

y=f(x)

, including the constant of integration. b. Use the initial condition to find the particular solution. c. Evaluate the particular solution at

x=6

. Express the final answer exactly, not as a decimal approximation.