APFIVE Solving An Initial Value Problem
All of the following are correct steps to solve $$\frac{dy}{dx} = 4*x$$ with initial condition $$y(1) = 3$$ except:
TITLE: Integration Rules Table: #000000
| Function | Antiderivative |
|---|---|
| $$4*x$$ | $$2*x^2$$ |
| $$x$$ | $$\frac{x^2}{2}+ C$$ |
A
After determining $$C$$, the particular solution represents a parabola passing through $$(1, 3)$$.
B
Integrating $$4*x$$ gives $$y = 2*x^2 + C$$, then using $$y(1) = 3$$ to solve for $$C$$.
C
Integrating $$4*x$$ directly gives $$y = 4*x + C$$.
D
The antiderivative of $$4*x$$ is $$2*x^2$$ because $$\frac{d}{dx}(2*x^2) = 4*x$$.
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