y^{''}+2y^'=0,y^'(0)=3,y(0)=0

Lösung

y^{^{''}} + 2 y^{^{'}} = 0, y^{^{'}} (0) = 3, y (0) = 0

y = \frac{3}{2} - \frac{3}{2} e^{- 2 t}

Schritte zur Lösung

y^{''} (t) + 2 y^{'} (t) = 0

Solve linear ODE:

y = \frac{3}{2} - \frac{3}{2} e^{- 2 t}

y = \frac{3}{2} - \frac{3}{2} e^{- 2 t}

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

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

2 y^{^{''}} + 6 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} + y^{^{'}} - 20 y = 0, y (0) = 1, y (0) = 22

y^{^{''''}} - 2 y^{^{'''}} + 2 y^{^{''}} - 2 y^{^{'}} + y = 0