$7\mathrm{.}41$ please!

$7\mathrm{.}14$ Find the current through a $50-nF$ capacitance if its voltage is $($a$)v=5(1-{10}^{4}t)V,($b$)v=10(1-e^{-{10}^{4}t})V,($c$)v=4sin{10}^{4}t,$ and $($d$)v=15V.$

$7\mathrm{.}41$ In the $RL$ circuit of Figure $7\mathrm{.}14($b$)$ let $R=1k,L=1$ mH $,$ and $i_S=10cos{10}^6$tmA. Find the complete response $i(t)$ if $($a$)i(0)=0,($b$)$ the initial stored energy in the inductance is $w(0)=12\mathrm{.}5nJ.($Beware that in $($b$)$ there are two such responses!$)$

Answer

$7\mathrm{.}41($a$)i(t)=7\mathrm{.}071cos({10}^{6}t-45)-5e^{-\frac{t}{1s}}mA$;

$($b$)i_1(t)=7\mathrm{.}071cos({10}^{6}t-45)mA,$ and $i_2(t)=i_1(t)-10e^{-\frac{t}{1s}}mA.$