y^{'''}-y^{''}+y^'-y=e^{-t}sin(t)

Lösung

y^{^{'''}} - y^{^{''}} + y^{^{'}} - y = e^{- t} sin (t)

y = c_{1} e^{t} + c_{2} cos (t) + c_{3} sin (t) - \frac{1}{5} e^{- t} cos (t)

Schritte zur Lösung

y^{'''} (t) - y^{''} (t) + y^{'} (t) - y = e^{- t} sin (t)

Solve linear ODE:

y = c_{1} e^{t} + c_{2} cos (t) + c_{3} sin (t) - \frac{1}{5} e^{- t} cos (t)

y = c_{1} e^{t} + c_{2} cos (t) + c_{3} sin (t) - \frac{1}{5} e^{- t} cos (t)

y^{^{''}} + y^{^{'}} - 30 y = 2 x

y^{^{''}} + 16 y = t^{2} + 1

y^{^{''}} - 2 y^{^{'}} + y = 3 x^{2} - 5

y^{^{''}} - 7 y^{^{'}} = t^{2}

y^{^{''}} - y^{^{'}} + 2 = 0