Find the general solution of the linear differential equation

Question

Quizplus · Accepted Answer

The linear differential equation given does not have any particular or initial conditions given, so we can assume it is a homogeneous equation of the form:
$$\frac{dy}{dx} + p(x)y = 0$$
where $p(x)$ is some function of $x$. Comparing this to the given equation, we can see that $p(x) = -\frac{1}{x}$. To solve this, we can use separation of variables:
$$\frac{dy}{y} = -p(x)dx$$
$$\ln|y| = \int \frac{1}{x}dx$$
$$\ln|y| = \ln|x| + C_1$$
$$|y| = e^{C_1}x$$
$$y = Cx$$
where $C = \pm e^{C_1}$ is the constant of integration. Therefore, the general solution to the given differential equation is $y=Cx$, where $C$ is a constant. The correct choice is B. Without the specific form of the differential equation given, it is impossible to determine the answer.

Find the General Solution of the Linear Differential Equation