y^{''}+3y^'-10y=0,y(0)=1,y^'(0)=30

Lösung

y^{^{''}} + 3 y^{^{'}} - 10 y = 0, y (0) = 1, y^{^{'}} (0) = 30

y = 5 e^{2 t} - 4 e^{- 5 t}

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) - 10 y = 0

Solve linear ODE:

y = 5 e^{2 t} - 4 e^{- 5 t}

y = 5 e^{2 t} - 4 e^{- 5 t}

y^{^{''}} - 20 y^{^{'}} + 101 y = 0, y (0) = 8, y^{^{'}} (0) = 1

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

\frac{1}{4} y^{^{''}} + \frac{7}{4} y^{^{'}} + \frac{5}{2} y = 0

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 0, y^{^{'}} (0) = 3

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