y^{''}+y^'-15y=0

Lösung

y^{^{''}} + y^{^{'}} - 15 y = 0

y = c_{1} e^{\frac{( - 1 + 61 ) t}{2}} + c_{2} e^{\frac{( - 1 - 61 ) t}{2}}

Schritte zur Lösung

y^{''} (t) + y^{'} (t) - 15 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{( - 1 + 61 ) t}{2}} + c_{2} e^{\frac{( - 1 - 61 ) t}{2}}

y = c_{1} e^{\frac{( - 1 + 61 ) t}{2}} + c_{2} e^{\frac{( - 1 - 61 ) t}{2}}

y^{^{''''}} - 4 y^{^{'''}} + 5 y^{^{''}} - 4 y^{^{'}} + 4 y = 0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 12 y = 0

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = 1, y^{^{'}} (0) = 2

(d^{2} + 4 d + 20)^{2} y = 0

y^{^{''}} + y^{^{'}} - 2 y = 0, y (0) = 6, y^{^{'}} (0) = 3