Solve the differential equation.

Question

Quizplus · Accepted Answer

The differential equation given is in the form of a separable differential equation. We can rewrite it as: $\frac{dy}{dt} = -\frac{y}{t}$.

Separating variables, we get: $\frac{1}{y} dy = -\frac{1}{t} dt$.

Integrating both sides, we get: $\ln|y| = -\ln|t| + C$.

Simplifying, we get: $\ln\frac{|y|}{|t|} = C$.

Exponentiating both sides, we get: $\frac{|y|}{|t|} = e^C$.

Simplifying, we get: $|y| = Ce^{|t|}$.

Since $|y|$ can take on positive or negative values, we can remove the absolute value and get the general solution: $y = Ce^{|t|}$, where $C$ is an arbitrary constant.

Therefore, the correct choice is B.

Solve the Differential Equation