y^{'''}+y^{''}-5y^'+3y=e^{-t}+sin(t)

Lösung

y^{^{'''}} + y^{^{''}} - 5 y^{^{'}} + 3 y = e^{- t} + sin (t)

y = c_{1} e^{- 3 t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{1}{8} e^{- t} + \frac{1}{20} sin (t) + \frac{3}{20} cos (t)

Schritte zur Lösung

y^{'''} (t) + y^{''} (t) - 5 y^{'} (t) + 3 y = e^{- t} + sin (t)

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{1}{8} e^{- t} + \frac{1}{20} sin (t) + \frac{3}{20} cos (t)

y = c_{1} e^{- 3 t} + c_{2} e^{t} + c_{3} t e^{t} + \frac{1}{8} e^{- t} + \frac{1}{20} sin (t) + \frac{3}{20} cos (t)

\frac{d ^{2} y}{d x ^{2}} + 100 y = 1000 sin (10 x)

y^{^{''}} - 2 y^{^{'}} + y = 4 x^{2} - 3 + x^{- 1} e^{x}

y^{^{''}} - y^{^{'}} + 324 y = 18 sin (18 t)

y^{^{'''}} - y^{^{'}} = 9 sin (t)

y^{^{''}} - 2 y^{^{'}} = 7 cos (3 t), y (π) = 5, y (0) = 0