I tried to solve a equation f(x). Finally I got a polynomial with coefficients.  (see Solve_for_coefficients.mw)

I want to find the values of unknown coeffients in the last polynomial equation as procedure to equating each cofficients to zero.

For example, the coefficients of x^2 is 1/48*(-24*p[2]+48*q[1]+24*q[2]+24) = 0.

Likewise, collect all the coefficients from x^0 to x^4 and solve them. Finally we get the coefficients value.

My question is How to collect the coefficients in this polynomial and solve this coefficients?

I tried to solve a hogher order ODE system to reduce first order ODE sytem. In this case I have assume a initial conditions as a variable. (sse the attachment, Conver_to_first_order.mw).

I got an error in specification of initial value...

How can I solve this problem in RKF45 method with shooting technique.

Here, I have assume f=x[1], f'=x[2]. f''=x[3], f'''=x[3]' and theta=x[4], theta'=x[5], theta''=x[5]'

I tried to solve a ODE system using rkf45 with shooting technique. But I have a lot of errors. How to resolve this...

See the attachment: Shoot_Blasius.mw

How to solve a ODE system using Newton's finite difference method?
How to plot f', theta and phi functions for various alpha values.

Difference.mw

How to convert a ploting values in a graph to excel?

restart;
with(PDETools): with(DETools): with(plots):with(plottools):
eq1 := ((D@@2)(f))(eta)*f(eta)*sin(alpha)+((D@@2)(f))(eta)*eta*cos(alpha)+2*((D@@3)(f))(eta) = 0;
ics := f(0) = 0, (D(f))(0) = 0, (D(f))(10) = 1; bcs := (D(f))(10) = 0, theta(10) = 0, phi(10) = 0;
Parameters1 := alpha = (1/3)*Pi;
sol1 := dsolve(eval({eq1, ics}, {Parameters1}), numeric);
p1 := odeplot(sol1, [[eta, ((D@@2)(f))(eta)]], eta = 0 .. 10, color = [red], axes = boxed);
display({p1});