| It is known to all that solving differential equation is a very meaningful thing, and the well-known Riccati equation is not only important of the application in the history , but also often appear in modern control theory and bifurcation theory of vector fields . As much as possible, engineering hope to find exact solutions, so these equations are still not losing its sense of the times, and has attracted many mathematicians'interest nowadays.Chapter I, Introduction: This chapter is mainly introduces the background and the research situation of the topics in our country and abroad.Chapter II, solving integral equations:(?)By the criterio nφ′( x)ψ(x)?mψ(x)ψ′(x)=0[1] of paper [1],,we will discuss the cases of three conditions, namely r =0; r =1, r≠0,1r =1,and get its general solution. In addition, when not satisfy the condition, if r =2, but satisfy the appropriate conditions, this equation is still integrable, and gives the general solution.Chapter III, solving integral equations: f m (G ( x ))∫a G ( x)f n( t )dt =φ(G ( x)), where m ( m+ n)>0and m + n≠?1,0. No discussion and only through the substitution ,it is transformed into Bernoulli equation, the paper find the general solution.And solving integral equations: (?). The paper discuss two cases and work out how to solve higher order differential equations. By varying ceiling function derivation, and substitution, to be translated into first order linear differential equations, the paper obtained a special solution of this equation, then do n-reintegration, at last get the general solution of the original equation.Chapter IV , solving a kind of integral function equations.According to the relationship between roots and coefficients, which will be in the form of three equations as a cubic function equations model, and variable substitution, and the literature [16] provides a formula to solve cubic equation, so we can get the original equations solution of combination form. Chapter V, The Development and Outlook of The Paper.
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