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

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Answer 1 · 2016-10-31T22:37:15

$y = f(x) = 2x^2 + 6$

Substitute $dy/dx$ for $f'(x)$

$dy/dx = 4x$

Use the separation of variable technique:

$dy = 4xdx$

Integrate both sides:

$y = 2x^2 + C$

Evaluate C, using the initial condition:

$6 = 2(0)^2 + C$

$C = 6$

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