y^{''''}-y=9t+cos(t)

Lösung

y^{^{''''}} - y = 9 t + cos (t)

y = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t) - 9 t - \frac{t sin ( t )}{4}

Schritte zur Lösung

y^{(4)} (t) - y = 9 t + cos (t)

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t) - 9 t - \frac{t sin ( t )}{4}

y = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t) - 9 t - \frac{t sin ( t )}{4}

y^{^{''}} - y = 2.9 cos (t), y (0) = 0, y^{^{'}} (0) = 2.9

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 5 y = e^{x}

\frac{d ^{2} y}{d t ^{2}} - 4 \frac{d y}{d t} + 4 y = e^{- 4 t}

y^{^{''}} + 8 y^{^{'}} + 15 y = - 6 cos (5 x)

y^{^{''}} - y = 2 + x^{2}