y^{''}+9y^'-20y=0,y(0)=1,y^'(0)=2

Lösung

y^{^{''}} + 9 y^{^{'}} - 20 y = 0, y (0) = 1, y^{^{'}} (0) = 2

y = (1 + \frac{13 - 161}{2 161}) e^{\frac{( - 9 + 161 ) t}{2}} - \frac{13 - 161}{2 161} e^{\frac{( - 9 - 161 ) t}{2}}

Schritte zur Lösung

y^{''} (t) + 9 y^{'} (t) - 20 y = 0

Solve linear ODE:

y = (1 + \frac{13 - 161}{2 161}) e^{\frac{( - 9 + 161 ) t}{2}} - \frac{13 - 161}{2 161} e^{\frac{( - 9 - 161 ) t}{2}}

y = (1 + \frac{13 - 161}{2 161}) e^{\frac{( - 9 + 161 ) t}{2}} - \frac{13 - 161}{2 161} e^{\frac{( - 9 - 161 ) t}{2}}

y^{^{''''}} + 5 y^{^{'''}} = 0

4 y^{^{''}} - 68 y^{^{'}} + 289 y = 0

y^{^{''}} + 9 y + y = 0, y (0) = 0.16, y^{^{'}} (0) = 0

y^{^{''}} - 7 y^{^{'}} - 2 y = 0

2 y^{^{''}} + 14 y^{^{'}} + 8 y = 0, y (0) = 5, y^{^{'}} (0) = 0