The equations that completely describe an electrical circuit are differential eq

Question

The equations that completely describe an electrical circuit are differential equations which can be derived from Kirchoff’s Laws. Using what is called the (Node Voltage Method) unknown voltages V1(t), V2(t), and V3(t) are applied to nodes in the circuit. Then we invoke Kirchoff’s law that says the sum of the currents at a node must be zero, and write the following three equations:

Transform the differential equations into the complex amplitude (phasor) form, and rearrange the equations as simultaneous linear equations with the unknown node voltages on the lefthand side (LHS), and the known voltage V0 on the righthandside (RHS).  In this step retain the symbols R and C for the resistance and capacitance values. Show all work 

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