y^{''''}-y=7t+cos(t)

Lösung

y^{^{''''}} - y = 7 t + cos (t)

y = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t) - 7 t - \frac{t sin ( t )}{4}

Schritte zur Lösung

y^{(4)} (t) - y = 7 t + cos (t)

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t) - 7 t - \frac{t sin ( t )}{4}

y = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t) - 7 t - \frac{t sin ( t )}{4}

y^{^{''}} + 3 y^{^{'}} + 2 y = 1, y (0) = 0, y^{^{'}} (0) = 0

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

y^{^{''}} - 4 y^{^{'}} = 2 e^{4 x}

y^{^{''}} + 16 y = 16, y (0) = 1, y^{^{'}} (0) = - 4

θ^{^{''}} (t) - θ (t) = t sin (t)