y^{''''}+2y^{'''}-5y^{''}-5y^'+1/2 y=0

Lösung

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

y = c_{1} e^{0.09188 \dots t} + c_{2} e^{- 0.92436 \dots t} + c_{3} e^{1.91179 \dots t} + c_{4} e^{- 3.07930 \dots t}

Schritte zur Lösung

y^{(4)} (t) + 2 y^{'''} (t) - 5 y^{''} (t) - 5 y^{'} (t) + \frac{1}{2} y = 0

Solve linear ODE:

y = c_{1} e^{0.09188 \dots t} + c_{2} e^{- 0.92436 \dots t} + c_{3} e^{1.91179 \dots t} + c_{4} e^{- 3.07930 \dots t}

y = c_{1} e^{0.09188 \dots t} + c_{2} e^{- 0.92436 \dots t} + c_{3} e^{1.91179 \dots t} + c_{4} e^{- 3.07930 \dots t}

y^{^{'''}} - 7 y^{^{''}} + 10 y^{^{'}} = 0

y^{^{'''}} + 6 y^{^{''}} - 16 y^{^{'}} = 0

625 x^{^{''}} + 100 x^{^{'}} + 3 x = 0, x (0) = 25, x^{^{'}} (0) = - 2

2 \cdot \frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 3 y = 0

16 y^{^{''}} - y = 0, y (- 4) = 1, y^{^{'}} (- 4) = - 1