y^{''}-6y^'+13y=0,y(pi/4)=1,y(0)=9

Lösung

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (\frac{π}{4}) = 1, y (0) = 9

y = e^{3 t} (9 cos (2 t) + \frac{1}{e ^{\frac{3 π}{4}}} sin (2 t))

Schritte zur Lösung

y^{''} (t) - 6 y^{'} (t) + 13 y = 0

Solve linear ODE:

y = e^{3 t} (9 cos (2 t) + \frac{1}{e ^{\frac{3 π}{4}}} sin (2 t))

y = e^{3 t} (9 cos (2 t) + \frac{1}{e ^{\frac{3 π}{4}}} sin (2 t))

y^{^{''''}} + 3 y^{^{'''}} + 2 y^{^{''}} + 6 y^{^{'}} = 0

1 y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (0) = 3, y^{^{'}} (0) = - 7

(d^{3} - d^{2} - 12 d) y = 0

x^{^{''}} + 4 x^{^{'}} + 4 x = 0, x (0) = 0, x^{^{'}} (0) = 2

15 y^{^{''''}} + 83 y^{^{''}} + 16 y = 0