Pretty much anything dynamics related. Starting basic displacements, velocity, acceleration integration for simple dynamic systems to more complicated equations for wind and spinning rotor interaction induced vibrations in wind turbines.
If you do not work with dynamics, for statics there are still a lot of encounters with deferential equations. Euler-Bernoulli Beam theory or plate and shell theories can be used for times when you want to solve more complex problems for which predefined equations do not exist and you do not have access to expensive fea software.
What do you use diff eq’s for on a daily basis?
Pretty much anything dynamics related. Starting basic displacements, velocity, acceleration integration for simple dynamic systems to more complicated equations for wind and spinning rotor interaction induced vibrations in wind turbines.
If you do not work with dynamics, for statics there are still a lot of encounters with deferential equations. Euler-Bernoulli Beam theory or plate and shell theories can be used for times when you want to solve more complex problems for which predefined equations do not exist and you do not have access to expensive fea software.