1/4 x^{''}-x=0,x(0)=1,x^'(0)=5

Lösung

\frac{1}{4} x^{^{''}} - x = 0, x (0) = 1, x^{^{'}} (0) = 5

x = (1 + \frac{3}{4}) e^{2 t} - \frac{3}{4} e^{- 2 t}

Schritte zur Lösung

\frac{1}{4} x^{''} (t) - x = 0

Solve linear ODE:

x = (1 + \frac{3}{4}) e^{2 t} - \frac{3}{4} e^{- 2 t}

x = (1 + \frac{3}{4}) e^{2 t} - \frac{3}{4} e^{- 2 t}

4 x^{^{''}} + 15 x^{^{'}} + 14 x = 0

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

3 y^{^{''}} + 4 y^{^{'}} + y = 0, y (0) = 2, y^{^{'}} (0) = - 1

y^{^{''}} - 7 y^{^{'}} + 12 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

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