12y^{''}-11y^'+2y=0,y(0)=7,y^'(0)=-3

Lösung

12 y^{^{''}} - 11 y^{^{'}} + 2 y = 0, y (0) = 7, y^{^{'}} (0) = - 3

y = (7 - \frac{92}{5}) e^{\frac{2 t}{3}} + \frac{92}{5} e^{\frac{t}{4}}

Schritte zur Lösung

12 y^{''} (t) - 11 y^{'} (t) + 2 y = 0

Solve linear ODE:

y = (7 - \frac{92}{5}) e^{\frac{2 t}{3}} + \frac{92}{5} e^{\frac{t}{4}}

y = (7 - \frac{92}{5}) e^{\frac{2 t}{3}} + \frac{92}{5} e^{\frac{t}{4}}

y^{^{''''}} - 4 y^{^{'''}} + 9 y^{^{''}} - 36 y^{^{'}} = 0

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

4 y^{^{''}} - y = 0, y (- 9) = 1, y^{^{'}} (- 9) = - 1

\frac{1}{16} y^{^{''}} + y^{^{'}} + 2 y = 0

y^{^{''}} + y^{^{'}} + \frac{1}{3} y = 0