Question

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3. Solve 2x2y" – 9xy' +12y = 0.

Answer 1

Given differendial eqr is 2x²y" - guy'ti2y=0 - 0 Z put 1=e - Inu=2 € dz an 1 2 dz mou dy dy dz ZP v are np LP IP KE xp - dz now р day da? dy d dre dal zá dy 22 d2 dudz ( 1/2 dy 11 12 - the se 14 hores de 1 - 1 / 2 de la .R hp 1 112 day dz2 72 de dz -> ae2d²y hp LP - da2 dz² d2 in ego 2 day put these values dy 2 dy 9 d22 dz +124 CO ap 2 dzy -> dy 11 d22 du +12y=0 This is second order differential equation with constant coefficiend. . corresponding n auxillary Boj is 24 2 2 m - 11 m +12 ^ - 8 -- 3 62m²-8m-3m +12=0 02m (*4)-3(7-4) = co =) (m-4) (2m-3)=0 -> a=noce oram-3=0 now on 2m-3 m-4 or m-3 2

solution of of ei is 42 CZ ci e 412 e Y12) z=Inse by back substitution 4lok => Yl2)=ci e (32) Inne + c2 e 312 2 + C2 => Y (21) = ci si This solation. is the required