I took Diffy Q about a year ago and that was the first math class that felt like a cookbook class. Ever since that class I feel like I've gotten worse and thinking less intuitive about math. I think I got discouraged because so many of those methods for solving in Diffy Q just popped up out of nowhere from someone much smarter than others (Euler/Lagrange). Now when I see a differential equation I just look up the method to solve it and apply. I can analyze my solution afterwards and see if it's correct but isn't there a better way to see a solution without these formal methods? I looked into geometry and differential equations because I'm a highly visual learner but those books/topics look far advanced for what I need. Now I'm learning about Laplace Transforms and we derived a couple easy ones but now we're gonna use a table to figure out the more complicated solutions.. My goal is not rigor but strong intuition in math and physics. I don't mind using a table for quick reference but I'd rather like to at least feel the correct solution from a intuitive geometrical sense. What can help me bring back my intuition of math? This semester I'm taking a math class on perturbation theory, transforms, and special functions and my hopes are it will help my math thinking but I'm not sure it will yet. I think I learned more about calculus and intuition from my physics classes than math classes. Has anyone else ever felt this way?