-6y^{''}+5y^'-1y=1t^2-1t+6e^2t

Lösung

- 6 y^{^{''}} + 5 y^{^{'}} - 1 y = 1 t^{2} - 1 t + 6 e^{2} t

y = c_{1} e^{\frac{t}{3}} + c_{2} e^{\frac{t}{2}} - t^{2} + (- 9 - 6 e^{2}) t - 33 - 30 e^{2}

Schritte zur Lösung

- 6 y^{''} (t) + 5 y^{'} (t) - 1 y = 1 t^{2} - 1 t + 6 e^{2} t

Solve linear ODE:

y = c_{1} e^{\frac{t}{3}} + c_{2} e^{\frac{t}{2}} - t^{2} + (- 9 - 6 e^{2}) t - 33 - 30 e^{2}

y = c_{1} e^{\frac{t}{3}} + c_{2} e^{\frac{t}{2}} - t^{2} + (- 9 - 6 e^{2}) t - 33 - 30 e^{2}

\frac{d ^{2} y}{d x ^{2}} + 2 y = 6 x, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} (p) + 6 y^{^{'}} (p) + 9 y (p) = p

y^{^{''}} - 2 y^{^{'}} - 35 y = 768 e^{- t}

y^{^{''}} - y^{^{'}} - 6 y = - e^{x} + 12

y^{^{''}} + 4 y = sec (22 x)