What you want to build is the mathematical model as shown in the figure. Wherein, taking the loop current I as a variable, uc=(∫idt)/C is obtained according to i=C×duc/dt, and then according to KVL:

R2×i+(∫idt)/C=u0 .

There is no problem in the mathematical process of solving problems, but for the analysis of dynamic circuits, differential equations are generally used to establish models. Therefore, when the current I is selected as a variable, the model becomes an integral equation, which is not easy to solve. The voltage uc of the capacitor should be chosen as a variable.

Therefore: i=C×duc/dt. ur=i×R2 .

The mathematical model is R2×C×duc/dt+uc=u0. The mathematical model is a differential equation, and the expression of uc can be obtained by solving the differential equation, and then the expression of I can be obtained.

Note: If it is a RL loop, the model of differential equation can be obtained by taking the inductance current iL as a variable.