@Kitonum  

plot this equation,

horizondal axis ->alpha range over -pi to pi;

vertical axis -> f'(x);

f(x)=-0.3075000000e-1*x^2-0.2145927617e-3*x^6-0.2692226562e-4*x^4+0.3750551906e-2*x^5+0.1050625000e-2*x^3-0.5266789021e-5*x^7+0.1082238239e-4*x^9-6.80130209*10^(-7)*x^6*sin(alpha)+0.2932994791e-5*x^6*cos(alpha)+0.4375000000e-2*x^4*cos(alpha)-0.7990625000e-4*x^5*sin(alpha)-0.1704062500e-3*x^5*cos(alpha)-3.907366066*10^(-7)*x^8*cos(alpha)^2-0.5000000000e-1*x^3*sin(alpha)+0.3375000000e-2*x^4*sin(alpha)-0.2231049199e-3*x^7*sin(alpha)+0.1723809524e-4*x^7*cos(alpha)^2-0.5000000000e-1*x^3*cos(alpha)+7.912017277*10^(-7)*x^8+0.4464285714e-3*x^7*cos(alpha)^3-0.6695959034e-3*x^7*cos(alpha)+0.4337937076e-4*x^9*cos(alpha)^2-0.982142856e-5*x^8*cos(alpha)^3+0.3392338088e-4*x^8*cos(alpha)+0.4906693567e-5*x^8*sin(alpha)+0.4412678315e-5*x^9*cos(alpha)+0.1833880452e-5*x^9*sin(alpha)+6.885206662*10^(-7)*x^10-0.1833333334e-3*x^6*cos(alpha)^2+.6*x+1.

@Kitonum  Thanks a lot.......

@Kitonum while doing the animation...

what to do?

@Mariusz Iwaniuk  In this case, how to solve this DE with  boundery condition is moveing?

@tomleslie  How to find the parameters values?

@Christian Wolinski  No,I am not tested this.

@Christian Wolinski  How to find unknown parameters n[1],n[2],n[3]?

@tomleslie  T= 1/k! *d^k/dx^k  is an operator.

T[u(x)]=U(k), u(x) is diff.k times with respect to x,which makes the result U(k),k  arbitrary integer. 

If we apply this operator, to given any function differentiate automatically .

Can you create the operator of this form?

@tomleslie doDiff:= diff(p(q), q$r) -> P(r); this case is possible?

@tomleslie  To use these commands, the mathematica must be installed?

@kencom1 Thank you for your cooperation.I know  differential transformation method.My question is how to convert differential equations into  differential transformation in maple. That is, maple codes  about differential transformation method.

I need some example