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

Lösung

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

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{10} sin (t) + \frac{1}{10} cos (t)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{10} sin (t) + \frac{1}{10} cos (t)

y = c_{1} e^{3 t} + c_{2} e^{- 3 t} - \frac{1}{10} sin (t) + \frac{1}{10} cos (t)

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = 6 x + 6 e^{- x}

2 y^{^{''}} + 4 y^{^{'}} + 2 y = sin (2 x) + 2 x cos (2 x)

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

y^{^{''}} - 5 y^{^{'}} - 6 y = x e - 5 x

\frac{1}{8} y^{^{''}} + 8 x + 4 y^{^{'}} = 0, y^{^{'}} (0) = 9, y (0) = 0