y^{''}-6y^'+9y=16e^7t,y(0)=7,y^'(0)=4

Lösung

y^{^{''}} - 6 y^{^{'}} + 9 y = 16 e^{7} t, y (0) = 7, y^{^{'}} (0) = 4

y = (7 - \frac{32 e ^{7}}{27}) e^{3 t} + (4 - \frac{- 16 e ^{7} + 189}{9}) t e^{3 t} + \frac{16 e ^{7} t}{9} + \frac{32 e ^{7}}{27}

Schritte zur Lösung

y^{''} (t) - 6 y^{'} (t) + 9 y = 16 e^{7} t

Solve linear ODE:

y = (7 - \frac{32 e ^{7}}{27}) e^{3 t} + (4 - \frac{- 16 e ^{7} + 189}{9}) t e^{3 t} + \frac{16 e ^{7} t}{9} + \frac{32 e ^{7}}{27}

y = (7 - \frac{32 e ^{7}}{27}) e^{3 t} + (4 - \frac{- 16 e ^{7} + 189}{9}) t e^{3 t} + \frac{16 e ^{7} t}{9} + \frac{32 e ^{7}}{27}

y^{^{''}} + 6 y + 34 = 0, y (0) = 3

y^{^{''}} + 2 y^{^{'}} - 3 y = 3 e^{2 t}

y^{^{''}} - 3 y^{^{'}} = 2 x - 2

y^{^{''}} + 4 y^{^{'}} + 5 y = - 15 x + e - x

y^{^{''}} + 2 y = t^{2} - 5, y (0) = 0, y^{^{'}} (0) = - 8