okay thank you sir. i tried to increase the degree to 10 but everytime i run the code, it keeps giving different output/values. how is that possible? i already try for 6, 7, 8 and 9 too and the result keeps changing.

@Carl Love 

i already changed the i and i can't find the approximate series for every variable. can someone enlightened me? i attached my work below. thank youHPM_Method.mw

@mmcdara 

it's worked! now can you help me to find the code for the series solution? thank you...

@tomleslie 

oh thank you! im trying to find the series solution by this method sir

@Carl Love 

thank you sir for the enlightment. im following this instructions because im new to Maple. Will you help me to get the approximate series solution with hpm please?