x^{''}+5x^'+3x=0,x(0)=5,x^'(0)=7

Lösung

x^{^{''}} + 5 x^{^{'}} + 3 x = 0, x (0) = 5, x^{^{'}} (0) = 7

x = (5 + \frac{39 - 5 13}{2 13}) e^{\frac{( - 5 + 13 ) t}{2}} - \frac{39 - 5 13}{2 13} e^{\frac{( - 5 - 13 ) t}{2}}

Schritte zur Lösung

x^{''} (t) + 5 x^{'} (t) + 3 x = 0

Solve linear ODE:

x = (5 + \frac{39 - 5 13}{2 13}) e^{\frac{( - 5 + 13 ) t}{2}} - \frac{39 - 5 13}{2 13} e^{\frac{( - 5 - 13 ) t}{2}}

x = (5 + \frac{39 - 5 13}{2 13}) e^{\frac{( - 5 + 13 ) t}{2}} - \frac{39 - 5 13}{2 13} e^{\frac{( - 5 - 13 ) t}{2}}

y^{^{''}} - 22 y^{^{'}} + 121 y = 0, y (0) = 0, y^{^{'}} (0) = 5

y^{^{''}} + 9 y^{^{'}} + 14 y = 0, y (0) = 0, y^{^{'}} (0) = - 1

y^{^{''}} + 10 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = - 9

5 y^{^{'}} + 6 y^{^{''}} = 0

y^{^{''}} - 400 y = 0