Equations containing derivatives are . . So to investigate topics like fluids dynamics, circuits, heat transfer, populations changes, vehicle trajectories, seismic waves, machine dynamics, . . A great many are not.
Solutions are functions.
If they can be expressed symbolically, they are mathematical formulas. Otherwise they are curves. Too many equations, too little time. What the course CAN do is help you to become familiar with some powerful methods and tools that you can use to investigate many kinds of differential equations. Some of them can be carried out with pencil and paper.