3y^{''}-15y^'+4y=0

Lösung

3 y^{^{''}} - 15 y^{^{'}} + 4 y = 0

y = c_{1} e^{\frac{( 15 + 177 ) t}{6}} + c_{2} e^{\frac{( 15 - 177 ) t}{6}}

Schritte zur Lösung

3 y^{''} (t) - 15 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( 15 + 177 ) t}{6}} + c_{2} e^{\frac{( 15 - 177 ) t}{6}}

y = c_{1} e^{\frac{( 15 + 177 ) t}{6}} + c_{2} e^{\frac{( 15 - 177 ) t}{6}}

1 y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 12 y^{^{'}} + 27 y = 0, y (0) = 1, y^{^{'}} (0) = - 12

18 y^{^{''}} + 9 y^{^{'}} - 5 y = 0

y^{^{''}} + 2 y^{^{'}} + 5 y = 0, y (0) = 3, y^{^{'}} (0) = 4

y^{^{'''}} + y^{^{''}} - 4 y^{^{'}} + 6 y = 0