y^{''}+y^'+y=13e^{-2t}(cos(t)+2sin(t))

Lösung

y^{^{''}} + y^{^{'}} + y = 13 e^{- 2 t} (cos (t) + 2 sin (t))

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

Schritte zur Lösung

y^{''} (t) + y^{'} (t) + y = 13 e^{- 2 t} (cos (t) + 2 sin (t))

Solve linear ODE:

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

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

y^{^{'''}} + 6 y = 7 y^{^{'}} + 4 e^{x}

y^{^{''}} + y - 12 = 0

x^{^{''}} - 3 x^{^{'}} + 2 x = 20 sin (2 t)

y^{^{''}} - 12 y^{^{'}} + 36 y = 8 e^{6 x}

x^{^{''}} - 5 x^{^{'}} + 6 x = 12, x (0) = 2, x^{^{'}} (0) = 0