Ieqn1=i10[t]==i1[t];
Ieqn2=i7[t]==i8[t]+i10[t];
Ieqn3=i1[t]+i8[t]==i2[t];
Ieqn4=i5[t]==i6[t];
Ieqn5=i2[t]+i9[t]==i3[t];
Ieqn6=i4[t]==i5[t];
Ieqn7=i3[t]==i4[t];
Ueqn1=R1*i1[t]==u1[t]-u3[t];
Ueqn2=i8[t]==C1*D[u2[t]-u3[t],t];
Ueqn3=i7[t]*R2==0-u2[t];
Ueqn4=u3[t]-u5[t]==L1*i2'[t];
Ueqn5=i9[t]==C2*D[0-u5[t],t];
Ueqn6=R4*i3[t]==u5[t]-u7[t];
Ueqn7=L2*i5'[t]==u6[t]-u4[t];
Ueqn8=R3*i6[t]==u4[t];
Ueqn9=us==u1[t]-u2[t];
Ueqn10=is==i4[t];

together={Ieqn1,Ieqn2,Ieqn3,Ieqn4,Ieqn5,Ieqn6,Ieqn7,Ueqn1,Ueqn2,Ueqn3,Ueqn4,Ueqn5,Ueqn6,Ueqn7,Ueqn8,Ueqn9,Ueqn10};
unknowns=Cases[together,_Symbol[t],{0,∞}]//Union
derivatives=Cases[together,_'[t],{0,∞}]//Union

together

values={R1->100,R2->100,R3->100,R4->10,C1->(10^(-6)),C2->2*(10^(-6)),L1->0.05,L2->0.01};

initialConditions=derivatives/.a_'[t]:>a[0]==0

f0=10000;
T=(1/f0);
inputVoltage=t^2*Tanh[200*(Sin[2*Pi*f0*t]+0.5)];
tmax=3T;
Plot[inputVoltage,{t,0,tmax}]
inputCurrent=t^2*Tanh[200*(Sin[2*Pi*f0*t]-0.5)];
Plot[inputCurrent,{t,0,tmax}]

StartingStepSize

eqns=together/.values/.{is->inputCurrent,us->inputVoltage}

NDSolve[Join[eqns,initialConditions],unknowns,{t,0,tmax},StartingStepSize->(10^(-5))]

Length[eqns]

Length[unknowns]

eqns