y^{''}-7y^'-4y=0

Lösung

y^{^{''}} - 7 y^{^{'}} - 4 y = 0

y = c_{1} e^{\frac{( 7 + 65 ) t}{2}} + c_{2} e^{\frac{( 7 - 65 ) t}{2}}

Schritte zur Lösung

y^{''} (t) - 7 y^{'} (t) - 4 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( 7 + 65 ) t}{2}} + c_{2} e^{\frac{( 7 - 65 ) t}{2}}

y = c_{1} e^{\frac{( 7 + 65 ) t}{2}} + c_{2} e^{\frac{( 7 - 65 ) t}{2}}

y^{^{''}} - 15 y^{^{'}} + 50 y = 0, y (0) = 8, y^{^{'}} (0) = - 55

y^{^{''}} + 10 y^{^{'}} + \frac{8}{3} y = 0, y (0) = 0, y^{^{'}} (0) = - 5

15 y^{^{''''}} + 32 y^{^{''}} + 9 y = 0

y^{^{''}} + 3 y^{^{'}} + 5 y = 0, y (0) = 4

y^{^{''}} + 4 y^{^{'}} - 5 y = 0, y (0) = 2, y^{^{'}} (0) = 14