# Homework help differential

$i_C(t) = C\\frac{dv(t)}{dt} \\\\
\\int_{t_0}^{\\tau} i_C(t)dt = C\\int_{t_0}^{\\tau} \\frac{dv(t)}{dt}dt \\\\
\\int_{t_0}^{\\tau} i_C(t)dt = C [ v(\\tau) - v(t_0) ] \\\\
v(\\tau) = \\frac{1}{C}\\int_{t_0}^{\\tau} i_C(t)dt + v(t_0)
$
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