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Question: solve by power seiries before doing these questions please it...

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SOLVE BY POWER SEIRIES

BEFORE DOING THESE QUESTIONS PLEASE IT IS MY HUMBLE REQUEST TO SOLVE ALL QUESTIONS STEP BY STEP PLEASE LABEL EACH STEP I AM DOING THIS FIRST TIME AND I DONT KNOW HOW TO DO IT I AM POSTING MY QUESTION 4TH TIME FIRST THREE TIMES I DIDNOT GET MY FULL ANSWERS AND DIDNOT GET MY ANSWERS STEP BY STEP PLEASE AFTER ONE STEP GIVE SOME EXPLANATION AND DO IN THAT WAY THAT I CAN DO ALL THESE KIND OF PROBLEMS AGAIN PLEASE DO NEAT HANDWRITING AND EXPLAIN EACH STEP AND LABEL THEM AS 1, 2 3 ETC.

1) (1- x^2)y'' - 2xy' + 2y = 0

THE SOLUTION IS y= a1x + a0(1 - x^2 - ( x^4 )/3 - ( x^6)/5 -...……………...).

2) y" + y= 0

the solution is a0cosx + a1sinx

3) y' - y=0

the solution is a0.e^x

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