y^{'''}-25y^'=te^{-5t}+6cos(5t)

Lösung

y^{^{'''}} - 25 y^{^{'}} = t e^{- 5 t} + 6 cos (5 t)

y = c_{1} + c_{2} e^{- 5 t} + c_{3} e^{5 t} + \frac{50 e ^{- 5 t} t ^{2} + 30 e ^{- 5 t} t + 7 e ^{- 5 t} - 120 sin ( 5 t )}{5000}

Schritte zur Lösung

y^{'''} (t) - 25 y^{'} (t) = t e^{- 5 t} + 6 cos (5 t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- 5 t} + c_{3} e^{5 t} + \frac{50 e ^{- 5 t} t ^{2} + 30 e ^{- 5 t} t + 7 e ^{- 5 t} - 120 sin ( 5 t )}{5000}

y = c_{1} + c_{2} e^{- 5 t} + c_{3} e^{5 t} + \frac{50 e ^{- 5 t} t ^{2} + 30 e ^{- 5 t} t + 7 e ^{- 5 t} - 120 sin ( 5 t )}{5000}

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{t ^{2} + 1}

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 13 t

y^{^{''}} + y^{^{'}} - 6 y = - 3 sin (x) + 4 e^{2 x}

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

y^{^{''}} - 25 y = sinh (5 x)