Video related to the solutions of ‘Exact Differential Equations’ it is useful for B.sc,M.sc Iit jam, csir net and other competative exams related to the mathematics.
A first order differential equation is one containing a firs but no higher derivative of the unknown function. For virtually every such equation encountered in practice, the general solution will contain one arbitrary constant, that is, one parameter, so a first order IVP will contain one initial condition. There is no general method that solves every first order equation, but there are methods to solve particular types.
Once a differential equation M dx + N dy = 0 is determined to be exact, the only task remaining is to find the function f ( x, y) such that f x = M and f y = N. The method is simple: Integrate M with respect to x, integrate N with respect to y, and then “merge” the two resulting expressions to construct the desired function f.
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