首先附上视频链接，讲得真的很好

{43i1+4(i1−i2)−ei=04(i2−i1)+3(i2−i3)+2i2=01c∫0ti3dt+3(i3−i2)=0\begin{cases} \frac{4}{3}i_1+4(i_1-i_2)-e_i=0 \\ 4(i_2-i_1)+3(i_2-i_3)+2i_2=0 \\ \frac{1}{c}\int ^{t}_0 i_3 dt + 3(i_3-i_2)=0 \end{cases} ⎩⎪⎨⎪⎧​34​i1​+4(i1​−i2​)−ei​=04(i2​−i1​)+3(i2​−i3​)+2i2​=0c1​∫0t​i3​dt+3(i3​−i2​)=0​另外显然

eo=2i2e_o=2i_2eo​=2i2​首先由第一个式子得

163i1−4i2=ei\frac{16}{3}i_1-4i_2=e_i316​i1​−4i2​=ei​

i1=316(ei+4i2)=316ei+34i2i_1=\frac{3}{16}(e_i+4i_2)=\frac{3}{16}e_i+\frac{3}{4}i_2i1​=163​(ei​+4i2​)=163​ei​+43​i2​

i1′=316ei′+34i2′{i_1}^{'}=\frac{3}{16}{e_i}^{'}+\frac{3}{4}{i_2}^{'}i1​′=163​ei​′+43​i2​′由第二个式子得

−4i1+9i2−3i3=0-4i_1+9i_2-3i_3=0−4i1​+9i2​−3i3​=0

i3=−43i1+3i2i_3=-\frac{4}{3}i_1+3i_2i3​=−34​i1​+3i2​

i3′=−43i1′+3i2′{i_3}^{'}=-\frac{4}{3}{i_1}^{'}+3{i_2}^{'}i3​′=−34​i1​′+3i2​′由第三个式子得

i3=3Ci2′−3Ci3′{i_3}=3C{i_2}^{'}-3C{i_3}^{'}i3​=3Ci2​′−3Ci3​′代入

i3=−43i1+3i2i_3=-\frac{4}{3}i_1+3i_2i3​=−34​i1​+3i2​

i3=3Ci2′−3Ci3′{i_3}=3C{i_2}^{'}-3C{i_3}^{'}i3​=3Ci2​′−3Ci3​′

−43i1+3i2=i3=3Ci2′−3Ci3′-\frac{4}{3}i_1+3i_2={i_3}=3C{i_2}^{'}-3C{i_3}^{'}−34​i1​+3i2​=i3​=3Ci2​′−3Ci3​′再由

i3′=−43i1′+3i2′{i_3}^{'}=-\frac{4}{3}{i_1}^{'}+3{i_2}^{'}i3​′=−34​i1​′+3i2​′

−43i1+3i2=3Ci2′−3C(−43i1′+3i2′)-\frac{4}{3}i_1+3i_2=3C{i_2}^{'}-3C(-\frac{4}{3}{i_1}^{'}+3{i_2}^{'}) −34​i1​+3i2​=3Ci2​′−3C(−34​i1​′+3i2​′)无脑化简

−43i1+3i2=3Ci2′+4Ci1′−9Ci2′-\frac{4}{3}i_1+3i_2=3C{i_2}^{'}+4C{i_1}^{'} -9C{i_2}^{'}−34​i1​+3i2​=3Ci2​′+4Ci1​′−9Ci2​′

−43i1+3i2=4Ci1′−6Ci2′-\frac{4}{3}i_1+3i_2=4C{i_1}^{'} -6C{i_2}^{'}−34​i1​+3i2​=4Ci1​′−6Ci2​′第二个式子和第三个式子已经用完了，磨刀霍霍向第一个式子

i1=316ei+34i2i_1=\frac{3}{16}e_i+\frac{3}{4}i_2i1​=163​ei​+43​i2​

−43i1+3i2=4Ci1′−6Ci2′-\frac{4}{3}i_1+3i_2=4C{i_1}^{'} -6C{i_2}^{'}−34​i1​+3i2​=4Ci1​′−6Ci2​′

−43(316ei+34i2)+3i2=4Ci1′−6Ci2′-\frac{4}{3}(\frac{3}{16}e_i+\frac{3}{4}i_2)+3i_2=4C{i_1}^{'} -6C{i_2}^{'} −34​(163​ei​+43​i2​)+3i2​=4Ci1​′−6Ci2​′

−14ei+2i2=4Ci1′−6Ci2′-\frac{1}{4}e_i+2i_2=4C{i_1}^{'} -6C{i_2}^{'} −41​ei​+2i2​=4Ci1​′−6Ci2​′我再代入

i1′=316ei′+34i2′{i_1}^{'}=\frac{3}{16}{e_i}^{'}+\frac{3}{4}{i_2}^{'}i1​′=163​ei​′+43​i2​′

−14ei+2i2=4C(316ei′+34i2′)−6Ci2′-\frac{1}{4}e_i+2i_2=4C(\frac{3}{16}{e_i}^{'}+\frac{3}{4}{i_2}^{'})-6C{i_2}^{'} −41​ei​+2i2​=4C(163​ei​′+43​i2​′)−6Ci2​′

−14ei+2i2=34Cei′−3Ci2′-\frac{1}{4}e_i+2i_2=\frac{3}{4}C{e_i}^{'}-3C{i_2}^{'} −41​ei​+2i2​=43​Cei​′−3Ci2​′结合显然的等式

eo=2i2e_o=2i_2eo​=2i2​

eo′=2i2′{e_o}^{'}=2{i_2}^{'}eo​′=2i2​′万事大吉

eo+32Ceo′=14ei+34Cei′e_o+\frac{3}{2}C{e_o}^{'}=\frac{1}{4}e_i+\frac{3}{4}C{e_i}^{'} eo​+23​Ceo​′=41​ei​+43​Cei​′