x^{''}-6x^'+9x=0

Lösung

x^{^{''}} - 6 x^{^{'}} + 9 x = 0

x = c_{1} e^{3 t} + c_{2} t e^{3 t}

Schritte zur Lösung

x^{''} (t) - 6 x^{'} (t) + 9 x = 0

Solve linear ODE:

x = c_{1} e^{3 t} + c_{2} t e^{3 t}

x = c_{1} e^{3 t} + c_{2} t e^{3 t}

y^{^{''}} + 144 y = 0

\frac{5}{8} x^{^{''}} + 40 x = 0

\frac{d ^{2} y}{d t ^{2}} - 4 \frac{d y}{d t} = 0

y^{^{''}} + 18 y^{^{'}} = 0, y (0) = 18

(0 + 1) y^{^{''}} + (7 + 1) y^{^{'}} - (6 + 1) y = 0