y^{''}-4y^'+40y=te^{2t}sin(6t)

Lösung

y^{^{''}} - 4 y^{^{'}} + 40 y = t e^{2 t} sin (6 t)

y = e^{2 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{- e ^{2 t} cos ( 6 t ) ( 72 t ^{2} - 12 t sin ( 12 t ) - cos ( 12 t ) ) + e ^{2 t} sin ( 6 t ) ( - 24 t cos ^{2} ( 6 t ) + 12 t + sin ( 12 t ) )}{1728}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) + 40 y = t e^{2 t} sin (6 t)

Solve linear ODE:

y = e^{2 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{- e ^{2 t} cos ( 6 t ) ( 72 t ^{2} - 12 t sin ( 12 t ) - cos ( 12 t ) ) + e ^{2 t} sin ( 6 t ) ( - 24 t cos ^{2} ( 6 t ) + 12 t + sin ( 12 t ) )}{1728}

y = e^{2 t} (c_{1} cos (6 t) + c_{2} sin (6 t)) + \frac{- e ^{2 t} cos ( 6 t ) ( 72 t ^{2} - 12 t sin ( 12 t ) - cos ( 12 t ) ) + e ^{2 t} sin ( 6 t ) ( - 24 t cos ^{2} ( 6 t ) + 12 t + sin ( 12 t ) )}{1728}

y^{^{''}} + 3 y^{^{'}} - 7 y = t^{4} e^{t}

x^{^{''}} - 16 x^{^{'}} + 64 x = t e^{8 t}

0.5 y^{^{''}} + 5 y^{^{'}} + 12 y = e^{- 4 t} (4 t - 2)

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

x^{^{''}} + 36 x = 8 cos (6 t)