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ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
Civil engineers use partial differential equations in many different situations. These include the following: heating and cooling; motion of a particle in a resisting medium; hanging cables; electric circuits; natural purification in a stream.
It is the solution of a differential equation without there being any restrictions on the variables (No boundary conditions are given). Presence of arbitrary constants indicates a general solution, the number of arbitrary constants depending on the order of the differential equation.
Yes, it is.
An Airy equation is an equation in mathematics, the simplest second-order linear differential equation with a turning point.