y^{'''}-4y^{''}-5y^'=0,y(1)=0,y^'(1)=8

解答

y^{^{'''}} - 4 y^{^{''}} - 5 y^{^{'}} = 0, y (1) = 0, y^{^{'}} (1) = 8

y = - (- 8 + 5 e^{5} c_{3}) - e^{5} c_{3} + e^{- t} (- 8 e + 5 e^{6} c_{3}) + c_{3} e^{5 t}

求解步骤

y^{'''} (t) - 4 y^{''} (t) - 5 y^{'} (t) = 0

求解线性方程:

y = - (- 8 + 5 e^{5} c_{3}) - e^{5} c_{3} + e^{- t} (- 8 e + 5 e^{6} c_{3}) + c_{3} e^{5 t}

y = - (- 8 + 5 e^{5} c_{3}) - e^{5} c_{3} + e^{- t} (- 8 e + 5 e^{6} c_{3}) + c_{3} e^{5 t}

y^{^{''}} - 1 y^{^{'}} + 0.1 y = 0

(d^{4} - 1) y = 0

4 y^{^{''}} - 2 y^{^{'}} - 2 y = 0, y (0) = 2, y^{^{'}} (0) = 1

u^{^{''}} + 49 H (t) = 0, H (0) = 3, u^{^{'}} (0) = - 7

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = 0, y (π) = 0