# How do you solve the differential equation given f'(x)=4x, f(0)=6?

How do you solve the differential equation given f'(x)=4x, f(0)=6?
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Deanna Randolph
Substitute $\frac{dy}{dx}$ for f'(x)
$\frac{dy}{dx}=4x$
Use the separation of variable technique:
$dy=4xdx$
Integrate both sides:
$y=2{x}^{2}+C$
Evaluate C, using the initial condition:
$6=2{\left(0\right)}^{2}+C$
$C=6$