In this paper, a microring resonator on silicon substrate with variable coefficients is proposed to solve the first order photonic differential equation.The ultrafine solution of the photonic differential equation with different coefficients is realized.Based on the coupled mode theory, the transfer function of microring resonator is analyzed in time domain and frequency domain.The etching depth is designed to be 220mm,and the silica-based ridge waveguide is designed to be 500mm. The shape of the micring-ring resonator is track type,which is composed of two semicircle sandwiches with two long straight waveguides.The radius of the semicircle is 30um,and the length of the straight waveguide is 60.75um.The a and b coefficient of differential equation can be adjusted,and the adjustment range is by fitting:1.5007e10 and :4.534e9.The simulation realizes the numerical solution process of the differential equation with different coefficient and the adjustment of electric control. After normalization,it compares with the real differential equation curve,and the error is less than 0.02.