This thesis project addresses two types of problems related 

with certain classes of differential equations matriarchal, 

such as the hypergeometric equation and the equation matriarchal 

matriarchal Ricati with coefficients of variables. 
The unifying element of memory is the method 

Frobenius matriarchal, which has already been used in the thesis 

doctoral M. Legua, R M. V. Ferrer and Company. The contribution 

This latest report is he marking error 

trncación of the solutions obtained in series, which 

to obtain two consequences of enormous interest in 

applications, such as: 
- Obtaining solutions computable in finite form. 
- The construction of approximate solutions to an accuracy 

preset. 
It must be said that the information I have, the analysis 

truncation error in terms of a fixed presicisión 

advance is not available in existing literature. 
In connection with the hypergeometric equation is matriarchal 

First get a couple of solutions to 

describe the general solution of (1.1) in terms of 

themselves, without considering the problem extended equivalent. Is 

also studied the truncation error when it gets 

solution in a series of initial value problem 

(1.1) and a representation of the function 

matriarchal hypergeometric function in terms of the Gamma 

matriarchal. 
The interest of the equation is a hypergeometric 

mergente continuation of the theory of polynomials otogonales 

matriarchal, because in the evaluation of the coefficients of the 

developments in series of orthogonal polynomials, they 

are expressed in terms of function 

hypergeometric. 
The Riccati equation is one of the most extensively studied for their 

emergence in classical and modern problems of theory 

control, as well as troubleshooting contour 

for linear systems (see the references in 

chapter devoted to the Riccati equation).