y^{''''}-y=14t+cos(t)

Lösung

y^{^{''''}} - y = 14 t + cos (t)

y = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t) - 14 t - \frac{t sin ( t )}{4}

Schritte zur Lösung

y^{(4)} (t) - y = 14 t + cos (t)

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t) - 14 t - \frac{t sin ( t )}{4}

y = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t) - 14 t - \frac{t sin ( t )}{4}

y^{^{''}} + y = - x^{- 2} sin (x) + 2 x^{- 1} cos (x)

y^{^{''}} + y = sin (x) sin (2 x)

y^{^{''}} - 3 y = e^{2 x} sin (5 x)

y^{^{''}} + 2 y^{^{'}} + 10 y = 17 sin (x) - 37 sin (3 x)

y^{^{''}} + 5 y + 6 y = 10 sin (x), y (0) = 1, y^{^{'}} (0) = - 4