Question

Solve the initial-value problem y'"' + y" - y - y = 0, y(0) = 5, y'(0) = 1, y" (0) = 9

Answer 1

Soin We can glll tyl-yl-y=0 y 10) = 5 y' (o)= y101= 9. Welte the Ausilany Equation m3 + m² -m-1=0 m2cm+1-1 (m+10=0 im? - 1) Lm +1) = 0 (m-1) ( m+ (M+1) = 0 171- we Know the repeated Moot 1-1-1 + e-t + tlzert en + y (4) = y'lt) ciet - 22e + + c3[t det? + ent dt dt y' (t) ciet -czet +63 [- tet tet] eqciis g' (t) = get_cge-t attze-t +get 8" (+) Geot + Get tetté + ]gt (zent y"(t) Get +Get thte-t the t + get .-2t yu(t) = Get tGo-t tzte ++he equi we putting gro) = 5 in the equation (1) Git (2+0 get OT (1+(2 eg (iv)

putting yıcol = 1 in the above equation (1) 1 G-C2+z putting yıllo) = in the above equii) 9=City to eq from eq and ea we get 9 = 5th 9-5=63 7 Cz = 4 from eq and eq we get - we 5 esits = -2 t cz 6 24 + 3 know that = 4 6 = 29, +4 6-4 26 = 20 q=1

putting the value above we get c=1 4 9 = 1 +₂ +4 g= 5+(2 24 y(t) = ce +Get+tget yet) lett - 4e-t t4te-t y (+) = et + 4 e-t + 4 tert
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