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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.
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What is the global solution of an ordinary differential equation?
The global solution of an ordinary differential equation (ODE) is a solution of which there are no extensions; i.e. you can't add a solution to the global solution to make it more general, the global solution is as general as it gets.
What is the local solution of an ordinary differential equation?
The local solution of an ordinary differential equation (ODE) is the solution you get at a specific point of the function involved in the differential equation. One can Taylor expand the function at this point, turning non-linear ODEs into linear ones, if needed, to find the behavior of the solution around that one specific point. Of course, a local solution tells you very little about the ODE's global solution, but sometimes you don't want to know that anyways.
What is a numerical solution of a partial differential equation?
Some partial differential equations do not have analytical solutions. These can only be solved numerically.
What is oscillatory solution in differential equations?
It happens when the solution for the equation is periodic and contains oscillatory functions such as cos, sin and their combinations.
Why do you need initial condition to solve differential equation?
The solution to a differential equation requires integration. With any integration, there is a constant of integration. This constant can only be found by using additional conditions: initial or boundary.
