y^{''}-6y+9y=t^2e^{3t}

Lösung

y^{^{''}} - 6 y + 9 y = t^{2} e^{3 t}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3 t} t ^{2}}{12} - \frac{e ^{3 t} t}{12} + \frac{1}{36} e^{3 t}

Schritte zur Lösung

y^{''} (t) - 6 y + 9 y = t^{2} e^{3 t}

Solve linear ODE:

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3 t} t ^{2}}{12} - \frac{e ^{3 t} t}{12} + \frac{1}{36} e^{3 t}

y = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{e ^{3 t} t ^{2}}{12} - \frac{e ^{3 t} t}{12} + \frac{1}{36} e^{3 t}

y^{^{''}} - 12 y^{^{'}} + 36 y = 14 e^{6 x}

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

y^{^{'''}} - y^{^{''}} - 25 y^{^{'}} + 25 y = 4 - e^{x} + e^{5 x}

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

y^{^{''}} + 4 y^{^{'}} + 4 = e^{- t}