Question

Solve the given third-order differential equation by variation of parameters. y" - 5y" – y' + 5y = e** y(x) =

Answer 1

Given that y" - sy'-y +54= зи We want to solve above equation by vantation of parameters method Auxiliary equation of given equation is m3.5 m² m+5=0 (m) (mt) (m-5)=0 Now, complementary burretion & CF le (F- Gent Gente su General solution of given differential equation is You = c.ftp. I You = ciellt get gen + Vientų eu tuera where U Wiery x gory dx wery W2rry V 2 -X goy du wery worry gery da wery where gery is RH. S ob given equation Voss way
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esu 0 W, cene, saj 0 Sesu Ѕи 25e an wilen, en, esnj=-4 e esh W2 (en ieu, esny s el en Sesa su en 95 W2(eh, eh, esny = - 4 e6n Wz (en en esny en en en O - en eu - waren, en esn) = -2
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With ging W(ehen, esn) -qen en dn q8 esn 27 vic + du 12 vi tean 24 waren, en, Snj gary Wren, en su du U2 = 02- - 4-еу 234 du. 18 esu tos endn U2 = tean 48 2n 103 - 48
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