@JLPaillet 

Thanks

would you write DTM format of this equation for me?I doubt it is right or not.

@John Fredsted

Hi John

I want to solve a problem with differential transformation method (DTM)

one of sentences of my equation is as I wrote it. transformation of this equation is contained of a dirac delta and I don't know how I should solve this problem.

Hi

i did it before but since that k and m are changable it should be used in brakets.

with parentheses code doesn't answer.

@mj1751 

Excuse me my friend

i found it myself,thanks a lot

@Carl Love 

if i want use a instead of 0.5 and b instead of 0.05,it means writing the equation parametrically,how should i write the code?

@Carl Love 

Thank you very much

this code is true

best regards

@Carl Love 

this is happened just for the first answer

@Carl Love 

for example the result of first equation is equal to -2.1 which the correct answer is -0.7

@Carl Love 

Hi

unfortuenately your code gives wrong result too.

the main equation is as follow:

with the initial conditon of theta[0]=1 and results as follow:

your code results are the same as mine and @mostafajani, they are wrong.

@mostafajani 

Hi

thank you for your comment

I have written my code as below:

restart;
F[0]:=1:
s1:=sum(F[k-m]*sum(F[m-L]*sum(F[L-j]*F[j],j=0..L),L=0..m),m=0..k):
eq:=(-1/(k+1))*(F[k]+0.5*sum((k-m+1)*F[k-m+1]*F[m],m=0..k)+0.05*s1):
n:=8:
for k from 0 to n do
F[k+1]:=solve(eq);
end do;

you have written in another way, but both of them get wrong results.

the results of this equation are 1,-0.7,0.19833,-0.0392777,0.01745,....

but with your and my code results are 1,-2.1,0.315,-0.4725,...

it means that series have been written wrong.

what's your opinion about it?