5y^{''}-6y^'+y=0,y(0)=5,y^'(0)= 1/5

Lösung

5 y^{^{''}} - 6 y^{^{'}} + y = 0, y (0) = 5, y^{^{'}} (0) = \frac{1}{5}

y = - e^{t} + 6 e^{\frac{t}{5}}

Schritte zur Lösung

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

Solve linear ODE:

y = - e^{t} + 6 e^{\frac{t}{5}}

y = - e^{t} + 6 e^{\frac{t}{5}}

x^{^{''}} + 4 x^{^{'}} + 8 x = 0

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

y^{^{''}} - b y = 0

49 y^{^{''}} - 168 y^{^{'}} + 144 y = 0

(D^{3} - 8) y = 0