y^{''}-6y^'+9y=0,y(0)=5,y^'(0)=12

Lösung

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 5, y^{^{'}} (0) = 12

y = 5 e^{3 t} - 3 e^{3 t} t

Schritte zur Lösung

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

Solve linear ODE:

y = 5 e^{3 t} - 3 e^{3 t} t

y = 5 e^{3 t} - 3 e^{3 t} t

25 y + 8 y^{^{'}} + y^{^{''}} = 0

\frac{4}{32} y^{^{''}} + 3 y^{^{'}} = 0

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

c \frac{d ^{2} y}{d x ^{2}} = y

2 x^{^{''}} + 72 x = 0