Differential equations can be used in Engineering in the following situations.
First-order ordinary differential equations can be used in modelling simple electrical circuits, projective motion and Newton’s Law of Cooling.
Second-order ordinary differential equations with constant coefficients can be used in modelling free (and forced) electrical and mechanical oscillations.
Deflection of a uniformly loaded beam
The formula for the defection of such a beam is given by
d^4y/dx^4 = W(x)/EI
where,
y is the deflection
x is the distance along the beam, measured from one end
W(x) is the uniformly distributed load along the beam
E is Young’s Modulus
I is the moment of inertia.
Differential equations also have applications in
Fluid Dynamics
-Design of Containers and Funnels
Heat Conduction Analysis
-Heat Spreaders in microelectronics
Combined Heat Conduction and Convection
-Design of Heating and Cooling Chanbers
Rigid-Body Dynamic Analysis