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 $$y = \frac{x^2}{2} + C$$.