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6y — 3y’ +y"—2y'=0 y" —Sy' +6y =0 iv’ — Sy’ + 6y = 0 17.y = x? + Ae** + Ber* Solution: 2 Arbitrary Constants (A and B) = 2 times you dif ferentiate Multiply both sides by e~** and dif ferentiate yew3* = x7e-3* + Ae + B . d yes (=) +e ty! = x2e73* (E29) +e73* (=) Ae* (E-») —Bye3* + ey? = —3x2e73* + 2xe-3* — Ae-* Multiply both sides by e* and dif ferentiate Bye7** 4 e72%y' = —3x7e72* 4 2ve72* — A d d arp ke a _ —2x,," y— 2X4 88 —2x,,7 _ 3ye (= 20)) Be **y" + ey" + oe ety (a 2x) P d d,., >, ( a& oe 2 2x ial mii -2x 2 o2x J 3x‘e ( 7 ( 23)) 3e (= (x )) + 2xe (Fe 2x)) +2e7% (= o) 6ye —2x _ 3e?*y! + e**y"" _ 2e-**y" = 6x%e72* — gre~2* — 4ye72* 4 2072" Simplify by multiplying e** both sides 6y — 3y’ + yy" — 2y' = 6x* — 6x —4x 42 y — Sy’ + 6y = 6x? - 10x +2 y" — Sy! + oy = 6x* — 10x +2 18.y = Cle* + Coxe* Solution: 2 Arbitrary Constants (C,and Cy ) > 2 times you dif ferentiate New Section | Page 4