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Gamma Function and its Properties, Beta Functions and its Properties, and related Topics.
Gamma Function and its Properties, Beta Functions and its Properties, and other topics.
Integral (log 1/x)^{n-1} dx , Integral x^{n-1}/(1 + x)^{m+n} dx, Beta(m,m), Integral x^{m-1}(Log 1/x)^{n-1} dx, Integral x^{m}(1-x^{n})^{p} dx, Integral x^{m}(Log x)^{n} dx, Integral x^{n}/n^{x} dx, Integral from a to b (x-a)^{m-1}(b-x)^{n-1} dx, and other topics.
Introduction to DE, Ordinary DE, Partial DE, Order, Degree, Formation of DE, Variable Separable DE, Concept of Particular and General Solution, Solving by Substitution, and other topics.
Homogeneous DE, Type dy/dx=(a1x+b1y+c1)/(a2x+b2y+c2), Type dy/dx=[K1(ax+by)+c1]/[K2(ax+by)+c2], and other topics.
First Order Linear DE, Solution of First Order Linear DE, DE of type f'(y)dy/dx + P(x)f(y) = Q(x), Bernoulli's Equation, and other topics.
Exact DE and Concept of Potential Function, Test for Exactness, Types of DEs Reducible to Exact form, and other topics.
Steps for Solving a general First Order DE, DE of Type dU(x,y) = dV(x,y), and other topics.
Leibnitz's Integral Rule and Introduction to DUIS, Typical Problems related to DUIS, and other topics.