y^{''}-18y^'+ay=0,y(0)=1,y^'(0)=17

Lösung

y^{^{''}} - 18 y^{^{'}} + a y = 0, y (0) = 1, y^{^{'}} (0) = 17

y = e^{t (9 + - a + 81)} (1 + \frac{- - a + 81 + 8}{2 81 - a}) - \frac{e ^{t (9 - - a + 81)} ( - - a + 81 + 8 )}{2 81 - a}

Schritte zur Lösung

y^{''} (t) - 18 y^{'} (t) + a y = 0

Solve linear ODE:

y = e^{t (9 + - a + 81)} (1 + \frac{- - a + 81 + 8}{2 81 - a}) - \frac{e ^{t (9 - - a + 81)} ( - - a + 81 + 8 )}{2 81 - a}

y = e^{t (9 + - a + 81)} (1 + \frac{- - a + 81 + 8}{2 81 - a}) - \frac{e ^{t (9 - - a + 81)} ( - - a + 81 + 8 )}{2 81 - a}

y^{^{''}} - 4 y^{^{'}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 3

y^{^{''}} + 12 y^{^{'}} + 36 y = 0, y (0) = 4, y^{^{'}} (0) = 0

x^{^{''}} + x = 0, x (0) = - 1, x^{^{'}} (0) = 2

y^{^{''}} + 3 y^{^{''}} - y^{^{'}} - 3 y = 0

(D^{2} - 3 D) y = 0