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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.
That depends on what type of equation it is because it could be quadratic, simultaneous, linear, straight line or even differential
A differential equation is a tool to certains carrers to find and solve all kinds of problems, in my case i'm a civil engineer and i use this tool to solve problems in the area of hidraulics, and in the area of structures. The differencial ecuations have all kinds of uses in the area of engieneering and in other fields too
Some expressions can't be factorised, and you have to use other methods to solve the equation.
There are different methods of using quadratic functions depending on the equation.