Slope Field And General Solution

The solution curves to $\frac{dy}{dx} = x$ are a family of parabolic curves shifted vertically by the constant C.

In the slope field for $\frac{dy}{dx} = x$, the slope at any point $(x,y)$ is equal to the x-coordinate.

When integrating $\frac{dy}{dx} = x$, the constant of integration must be zero.

Integrating $\frac{dy}{dx} = x$ yields $y = \frac{x^2}{2} + C$.