1/2 x^{''}+3/2 x^'+x=0

Lösung

\frac{1}{2} x^{^{''}} + \frac{3}{2} x^{^{'}} + x = 0

x = c_{1} e^{- t} + c_{2} e^{- 2 t}

Schritte zur Lösung

\frac{1}{2} x^{''} (t) + \frac{3}{2} x^{'} (t) + x = 0

Solve linear ODE:

x = c_{1} e^{- t} + c_{2} e^{- 2 t}

x = c_{1} e^{- t} + c_{2} e^{- 2 t}

y^{^{''}} + 2 y^{^{'}} + 100 y = 0

\frac{24}{32} x^{^{''}} + 6 x = 0, x (0) = 0.5, x^{^{'}} (0) = 0

\frac{d ^{4} y}{d x ^{4}} - \frac{d y}{d x} = 0

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

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