y^{''}+8y^'+16y=0,y(0)=5,y^'(0)=23

Lösung

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 5, y^{^{'}} (0) = 23

y = 5 e^{- 4 t} + 43 t e^{- 4 t}

Schritte zur Lösung

y^{''} (t) + 8 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = 5 e^{- 4 t} + 43 t e^{- 4 t}

y = 5 e^{- 4 t} + 43 t e^{- 4 t}

2 y^{^{''}} - 13 y^{^{'}} + 20 y = 0, y (0) = - 2, y^{^{'}} (0) = - 11

4 y^{^{''}} + 20 y^{^{'}} + 29 y = 0, y (1) = 8

y^{^{''}} - 3 y^{^{'}} + α y = 0, y (0) = 1, y^{^{'}} (0) = 5

6 y^{^{''}} + y^{^{'}} - 2 y = 0, y (1) = 2, y^{^{'}} (1) = \frac{1}{6}

x^{^{''}} - 0.1 x^{^{'}} + 1.0025 x = 0