% Define the symbolic variables
syms v1 v2 v3
% Given values
R1 = 1/3; % Resistance in Ohms
R2 = 1/2; % Resistance in Ohms
R3 = 1/6; % Resistance in Ohms
I1 = 4; % Current in Amps
I2 = 9; % Current in Amps
V_source = 5; % Voltage source value in Volts
% KCL equations using the supernode method
% Equation at node v1:
eq1 = (v1 - v2) / R1 == I1;
% Equation at node v3:
eq2 = (v3 - v2) / R3 == -I2;
% Supernode: Combine v2 and v3 with voltage source constraint
% Voltage constraint: v3 = v2 + V_source
eq3 = v3 == v2 + V_source;
% KCL at the supernode (combining v2 and v3):
% (v2 - v1) / R1 + v2 / R2 + (v2 - v3) / R3 = 0
eq4 = (v2 - v1) / R1 + v2 / R2 + (v2 - v3) / R3 == 0;
% Solve the equations
sol = solve([eq1, eq2, eq3, eq4], [v1, v2, v3]);
% Display the results
v1_sol = double(sol.v1);
v2_sol = double(sol.v2);
v3_sol = double(sol.v3);
fprintf('The solution for v1 is: %.2f V\n', v1_sol);
fprintf('The solution for v2 is: %.2f V\n', v2_sol);
fprintf('The solution for v3 is: %.2f V\n', v3_sol);
