Final Answer:
The general solution to the differential equation y" - 3y' = 0 is y = C₁e^(3x) + C₂e^(0x), where C₁ and C₂ are arbitrary constants.
Step-by-step explanation:
This differential equation is a second-order homogeneous linear differential equation with constant coefficients. The characteristic equation is:
r² - 3r = 0
Factoring the equation, we get:
(r-3)(r-0) = 0
Therefore, the roots of the characteristic equation are r = 3 and r = 0.
Since we have two distinct roots, the general solution of the differential equation can be written as a linear combination of two exponential terms:
y = C₁e^(3x) + C₂e^(0x)
where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions.