A function satisfies the differential equation dy dx = 3y x

MATHEMATICS · Multi-part · CBSE · Mathematics · Differential Equations · Differential Equations

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

. (1) Determine the general solution in explicit form

y=f(x)

, including the constant of integration. (2) Use the initial condition to find the particular solution. (3) Evaluate the particular solution at

x=6

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