In this article we introduce the software SimKinet, a free tool specifically designed to solve systems of differential equations without any programming skill. The underlying method is the so-called Network Simulation Method, which designs and solves an electrical network equivalent to the mathematical problem. SimKinet is versatile, fast, presenting a real user-friendly interface, and can be employed for both educational and researching purposes. It is particularly useful in the first courses of different scientific degrees, mainly Chemistry and Physics, especially when facing non-analytic or complex-dynamics problems. Moreover, SimKinet would help students to understand fundamental concepts, being an opportunity to improve instruction in Chemistry, Mathematics, Physics and other Sciences courses, with no need of advanced knowledge in differential equations. The potency of SimKinet is demonstrated via two applications in chemical kinetics: the photochemical destruction of stratospheric ozone and the chaotic dynamics of the peroxidase-oxidase reaction.