Engineering Open Modelica, work with an RLC-circuit

[Lotos]

Homework Statement

Convert one RLC graph to another using equations

Relevant Equations

dIL/dt=(Uin-R*IL-Uc)/L;
dUc/dt=IL-Iout/C

Good day.
I am studying Open Modelica and building RLC.
I was given the following task:

From the initial network

make one (sample graphics on Scilab but needs in Open Modelica)

As you can see in the graph that is presented in scilab, the graphs start from different points.
Here is a list of equations that I implement in the Open Model for the 1st figure(Working,the main example in Modelica)

model Lab5

extends Modelica.Icons.Example;
type Voltage=Real(unit="V");
type Current=Real(unit="A");
type Resistance=Real(unit="Ohm");
type Capacitance=Real(unit="F");
type Inductance =Real(unit="H");

parameter Modelica.SIunits.Resistance R=100 "Resistance";
parameter Modelica.SIunits.Inductance L=1 "Inductance";
parameter Modelica.SIunits.Voltage Vb=24 "Total DC Voltage";
parameter Modelica.SIunits.Capacitance C=1e-3 "Capacitance";
Voltage V;
Current i_L;
Current i_R;
Current i_C;

equation
V = i_R * R;
C * der(V) = i_C;
L * der(i_L) = Vb - V;
i_L = i_R + i_C;

And these are attempts to implement for my assignment(not working and buildin)

extends Modelica.Icons.Example;
type Voltage=Real(unit="V");
type Current=Real(unit="A");
type Resistance=Real(unit="Ohm");
type Capacitance=Real(unit="F");
type Inductance =Real(unit="H");

parameter Modelica.SIunits.Resistance R=100 "Resistance";
parameter Modelica.SIunits.Inductance L=1 "Inductance";
parameter Modelica.SIunits.Voltage Vb=24 "Total DC Voltage";
parameter Modelica.SIunits.Capacitance C=1e-3 "Capacitance";

Current u_Vx;
Current u_L;
Current u_R;
Current u_C;
Current i_Vx;
Current i_L;
Current i_R;
Current i_C;

equation
i_L=i_C+i_Vx;
i_R=i_L;
u_L=u_R+u_C;
u_Vx=u_L;
C*der(u_C)=i_C;
L*der(i_L)=u_L;
der(i_L)=(u_Vx-R*i_L-u_C)/L;
der(u_C)=(i_L-i_Vx)/C;

I know, that is this equations errors(a lot of variables, but not enought equations) and wrong scheme for solving equations.
What and how do I need to fix my equations?

 

[Lotos]

Modified the code a little to match the calculations and variables.

model Lab5
  extends Modelica.Icons.Example;
  type Voltage=Real(unit="V");
  type Current=Real(unit="A");
  type Resistance=Real(unit="Ohm");
  type Capacitance=Real(unit="F");
  type Inductance =Real(unit="H");
 
  parameter Modelica.SIunits.Resistance R=100 "Resistance";
  parameter Modelica.SIunits.Inductance L=1 "Inductance";
  parameter Modelica.SIunits.Voltage Vb=24 "Total DC Voltage";
  parameter Modelica.SIunits.Capacitance C=1e-3 "Capacitance";
  Current u_Vx;
  Current u_L;
  Current u_R;
  Current u_C;
  Current i_Vx;
  Current i_L;
  Current i_R;
  Current i_C;
 
equation 
  i_L = 5;
  u_C =3;
  i_R=i_L+i_Vx+i_C;
  u_Vx=u_L+u_R+u_C;
 
  C*der(u_C)=u_C; 
  L*der(i_L)=i_L; 
  der(i_L)=(u_Vx-R*i_L-u_C)/L;
  der(u_C)=(i_L-i_Vx)/C;  annotation(
    uses(Modelica(version = "3.2.3")));
end Lab5;

But the following errors appeared

Internal error IndexReduction.pantelidesIndexReduction failed! Found empty set of continuous equations. Use -d=bltdump to get more information.
Internal error Transformation Module PFPlusExt index Reduction Method Pantelides failed!