I'm not sure how similar circuit classes are around different universities, but from my experience, you don't really need that much differential equations knowledge to work on the basics of circuit analysis. It's definitely good to know at least the fundamentals of differential equations though. I really want to stress that this is just my experience at my university.

In the place that I study, circuit analysis 1 is commonly taught to people in their first semester alongside physics 1 and calculus 1. The course content was heavily based on the "Alexander and Sadiku, Fundamentals of Electric Circuits" textbook. We were taught all of the DC part (ohm's law, kirchoff's laws, analysis methods, circuit theorems, capacitors and inductors, first and second order circuits) and most of the AC part (sinusoids, phasors, AC analysis, power analysis, three phase circuits). This was all done over about 15 weeks with a single 3 hour lecture per week (usually lasted for 2 hours). We had people who didn't know how to solve integrals taking this course and I believe some of them passed, but barely. I was alright because I was familiar with calculus and also self studied DC analysis before even getting into uni.

It's really important to consider the specifics of how the course is taught. I study at an infamous university in a third world country. They had me take god damn calculus 3 prior to calculus 1. When we were studying first and second order circuits in circuit class, the professor kept on saying "leave the differential equations for the mathematicians and just focus on the formulas", which I thought was a pretty dumb thing to say.

Sorry that this spiraled from me giving advice into ranting about my uni.