x^{''}-6x+9x=126t^2e^{3t}

Lösung

x^{^{''}} - 6 x + 9 x = 126 t^{2} e^{3 t}

x = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{21 e ^{3 t} t ^{2}}{2} - \frac{21 e ^{3 t} t}{2} + \frac{7}{2} e^{3 t}

Schritte zur Lösung

x^{''} (t) - 6 x + 9 x = 126 t^{2} e^{3 t}

Solve linear ODE:

x = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{21 e ^{3 t} t ^{2}}{2} - \frac{21 e ^{3 t} t}{2} + \frac{7}{2} e^{3 t}

x = c_{1} cos (3 t) + c_{2} sin (3 t) + \frac{21 e ^{3 t} t ^{2}}{2} - \frac{21 e ^{3 t} t}{2} + \frac{7}{2} e^{3 t}

y^{^{''}} + 9 \cdot y^{^{'}} = 5 t

y^{^{''}} + 5 y^{^{'}} + 25 \cdot y = - 9.81

y^{^{''}} - 3 y^{^{'}} - 4 y = 8 e^{t} cos (2 t)

3 y^{^{''}} + 27 y = 2 cos (4 x)

y^{^{'''}} - 3 y^{^{''}} + 4 y^{^{'}} - 12 y = 13 e^{3 x}