Find the general solution of the linear differential equation

Question

Quizplus · Accepted Answer

The given differential equation is in the form 
$$\frac{dy}{dx} + 3y = 0$$
This is a first-order linear differential equation with constant coefficients. The general solution of such an equation is given by
$$y(x) = Ce^{-\int 3dx} = Ce^{-3x}$$
where $C$ is the constant of integration. Therefore, the correct choice is (C). Without knowing the specific form of the differential equation, we can determine the general solution simply by counting the number of arbitrary constants that appear in the final answer. The correct answer must have exactly one arbitrary constant for a first-order linear differential equation. Therefore, options A, B, and D can be eliminated because they have either no arbitrary constants (option A) or two arbitrary constants (options B and D). In option E, there are three arbitrary constants, which is not possible for a first-order linear differential equation. Option C is the only remaining choice, and it has exactly one arbitrary constant, which means it is the correct solution.

Find the General Solution of the Linear Differential Equation