Dear all
I have an algorithm  to solve a first order odes, all steps of the algorithm ( as presented in the book are coded) but unfortunately something wrong. 
The algorithm and the code are attached in the following code. 
Thank you in advantage for your help. 

sol_odes.mw

Dear all
My goal, is expand a given function using chebyshev polynomails. Everything is well written, but unfortynattely, the coeffients an, are not computed exactly, but the result return only integral form and there is evalaution of this integral.

How, can I expand my function f , using sum ( a_n chebyshev Tn), for x in [0,1] and we get explicitely the results. 

Question_integral_chebyshev.mw

Thank you for any help 

Dear all;

I have a data, I would like to save this data in a table with labeled columns and  each column contains the corresponding values.

cretae_tabl.mw

thank you for your help 

Dear all

I would like to compute the monomial polynomial in taylor series, I tried 
f:=cos(t);

fn:=n->subs(diff(f(x),x$n),x=0)/factorial(n);
but it is does not work 
anay help please

Dear all

I solve a first order nonlinear ode, using dsolve but there is no solution obtained.

problem_dsolve.mw
How, can I get the exact solution.

tahnk you for your help