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4. Method of variable reduction makes use of one of the known solutions of a differential equation to find the other solution

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Given ditterential equation is (x-1yxyy=o one solution now & let 2(x) Solut u ex .y20x ue ue 2. y=uex +exu + ule%+ e* u 2 utnis eqn Can Solve Now we bychange ot vasiable inro ducina nes variable Such chat vu ditterential ean oecomes OS x-1 V x-2)(InCx-)-X [Kconstant o interah V= ke In(x-1) V ke V- ке х Сх-7 VkEe nous 1 u-Ke e xe*]+c uKx eC hous we can choose constanbsnouslet K 1 u -x e X = -x exe uex 20x)=-X solution tdY ditferenHaf equation is wyitten as A YI () 2 Y2 ( AE Bx

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