4y^{''}+16y^'+1/16 y=0

Lösung

4 y^{^{''}} + 16 y^{^{'}} + \frac{1}{16} y = 0

y = c_{1} e^{\frac{( - 16 + 255 ) t}{8}} + c_{2} e^{- \frac{( 16 + 255 ) t}{8}}

Schritte zur Lösung

4 y^{''} (t) + 16 y^{'} (t) + \frac{1}{16} y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 16 + 255 ) t}{8}} + c_{2} e^{- \frac{( 16 + 255 ) t}{8}}

y = c_{1} e^{\frac{( - 16 + 255 ) t}{8}} + c_{2} e^{- \frac{( 16 + 255 ) t}{8}}

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 10, y^{^{'}} (0) = 0

y^{^{''}} - 4 y = 0, y (0) = 6, y^{^{'}} (0) = 0

y^{^{''}} + 49 y = 0, y (0) = 2, y^{^{'}} (0) = 1

y^{^{''}} - 4 y + 3 y = 0, y (0) = - 1, y^{^{'}} (0) = - 5

y^{^{''}} + 4 y^{^{'}} + 20 y = 0, y (0) = 6, y^{^{'}} (0) = - 11