Depends heavily on the teacher.
I loved calculus at the junior college I attended. I had two extremely talented professors who made the subject both fun and interesting. The text was excellent. While rigorous, it was extremely well presented. I got As & Bs.
Then I got to the big 4 year school. My differential equations class was taught by indifferent grad students. The text was utter crap. We spent nearly an entire quarter on first order equations with a week or two devoted to second order. (This is functionally useless to engineers.)
I took and dropped the course twice. The third time, I gutted it out and passed - with a C.
Engineers need an understanding of differential equations because they are the mathematics that describe dynamic systems. What happens to a bridge subjected to dynamic loads, or how an electrical circuit will react to certain inputs, etc., is described by differential equations. My crappy diff-eq class handicapped my visceral understanding of dynamic systems.
I actually LEARNED differential equations in a senior level automatic control systems class. In a week I learned a thousand times what was taught in diff-eq. Enough to enable me, a gear head, to design and build a fourth order active filter network used in my high dollar stereo system to eliminate the effects of record warp.
The teacher and presentation makes all the difference.
Ah, engineers, so much knowledge, so little wisdom.
Computers can do what you're suggesting. The purpose of the class is to tell you why. I'm not saying they weren't bad teachers, but first order ODEs are the only way you can understand issues like the existence and uniqueness of solutions without bogging yourself down in the details.
Second order ODEs are nothing once you understand the theory, it's just computation -- monkey work. And the specific applications happen later. You don't learn to build a house by learning how to build a cape cod and then start from scratch learning to build a rancher.
I submit that you probably learned a lot more in your ODE class than you realized. It's like the difference between learning how to be a computer programmer and how to use MSWord. You just wanted to learn MSWord. It doesn't make the basic C++ course a bad one.
Yeah, here's the other thing. It is very unlikely that you would have passed a calc test at the 4 year school. Calc classes at junior college go much more slowly and present much less material.