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INITIAL VALUE PROBLEMS FOR NON-HOMOGENEOUS ODE

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 6TH TIME FIRST FIVE 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)    Y" + Y = 0.001 X^2    WHERE    Y( 0 ) = 0    AND Y'( 0 )= 1.5

THE ANSWER IS Y= 0.002 COS X + 1.5 SIN X + 0.001 X^2 - 0.002

2)    Y" + 3Y' + 2.25Y = -10 e^-1.5x WHERE Y( 0 )= 1    AND    Y' ( 0 )= 0

THE ANSWER IS    Y    = ( 1 + 1.5X )e^1.5X - 5X^2

3)    Y" + 2Y' + 5Y = e^1.5X + 40 COS 10X - 190 SIN 10X WHERE Y( 0 ) = 0.16 AND    Y'(0) = 40.08

THE ANSWER IS    Y= 10 e^(-X ) SIN2X + 0.16 e^0.5X + 2SIN 10X

PLEASE EXPLAIN EACH STEP IN NEAT HANDWRITING I AM PREPARING FOR MY FINALS I AM DOING THIS FIRST TIME PLEASE, PLEASE ,PLEASE EXPLAIN IN SUCH A WAY THAT I CAN DO ALL KIND OF THESE QUESTIONS .

I SHALL BE VERY GREATFULL TO YOU DONT FORGET TO LABEL STEPS

SIR PLEASE DO EACH AND EVERY STEP CLEAR BECAUSE THE PERSONS THAT GIVE ME ANSWER WAS ONLY ANSWER AND THEY ARE NOT REPLYING TO MY COMMENT THEY ONLY WASTE MY QUESTIONS I COMPLAINED FOR THEM AND PLEASE I REQUEST YOU TO GIVE ALL ANSWERS WITH EXPLANATION OF EACH STEP I REQUEST YOU TO ALLOW ME TO COMMENT SO I CAN DISCUSS MY CONFUSIONS IN THE QUESTION WITH YOU PLEASE DO ALL QUESTIONS WITH EXPLAINING EACH STEP I WANT TO LEARN THE TECHNIQUE REPLY ME AS SOON AS POSSIBLE TOMMOROW IS MY FINAL EXAM