Find the solution to the following separable differential equation. , a is a constant

Question

Find the solution to the following separable differential equation.  , a is a constant

Quizplus · Accepted Answer

The given differential equation is separable, meaning we can write it in the form of

$$\frac{dy}{dx} = a y^2$$

We can then separate the variables and integrate both sides with respect to their respective variables:

$$\int \frac{1}{y^2} dy = \int a dx$$

$$-\frac{1}{y} = ax + C$$

where $C$ is the constant of integration. We can solve for $y$ to get

$$y = -\frac{1}{ax + C}$$

Since $a$ and $C$ are constants, the answer is B.

Find the Solution to the Following Separable Differential Equation