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

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

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

Quizplus · Accepted Answer

The given differential equation is:
$$y\frac{dy}{dx}=ax.$$
Separating the variables and integrating, we get
$$\int ydy=\int axdx$$
$$\frac{1}{2}y^2=\frac{a}{2}x^2+C$$
where C is the constant of integration.
Solving for y, we get
$$y=\sqrt{ax^2+C}.$$
Therefore, the solution is
$$y=\sqrt{ax^2+C}.$$ 
So, the correct choice is B.

Find the Solution to the Following Separable Differential Equation