Slope Field And General Solution

Question

All of the following statements regarding the slope field and antiderivative of $$\frac{dy}{dx} = x$$ are true except:

Accepted Answer

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

Answer

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

Answer

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

Answer

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