APFIVE Solving An Initial Value Problem
All of the following statements about solving the initial value problem $$\frac{dy}{dx} = 4x$$ with the initial condition $$y(1) = 3$$ are correct EXCEPT:
A
Integrating $$4*x$$ gives $$y = 2*x^2 + C$$, then using $$y(1) = 3$$ to solve for $$C$$.
B
The antiderivative of $$4*x$$ is $$2*x^2$$ because $$\frac{d}{dx}(2*x^2) = 4*x$$.
C
After determining $$C$$, the particular solution represents a parabola passing through $$(1, 3)$$.
D
Integrating $$4*x$$ directly gives $$y = 4*x + C$$.
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