y^{''}+y^'=sinh(t)

Lösung

y^{^{''}} + y^{^{'}} = sinh (t)

y = c_{1} + c_{2} e^{- t} + cosh (t) + e^{- t} (- e^{t} sinh (t) + \frac{1}{2} t + \frac{1}{4} e^{2 t})

Schritte zur Lösung

y^{''} (t) + y^{'} (t) = sinh (t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + cosh (t) + e^{- t} (- e^{t} sinh (t) + \frac{1}{2} t + \frac{1}{4} e^{2 t})

y = c_{1} + c_{2} e^{- t} + cosh (t) + e^{- t} (- e^{t} sinh (t) + \frac{1}{2} t + \frac{1}{4} e^{2 t})

y^{^{''}} - 2 \cdot y^{^{'}} + 2 \cdot y = cos (t), y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} + 6 y = t, y (0) = - 3, y^{^{'}} (0) = 0

3 y^{^{''}} + 2 y^{^{'}} + 1 = 0

y^{^{''}} - y^{^{'}} - 6 y = e^{- 3 x} (7 - 8 x + 6 x^{2})

y^{^{''}} - 2 y^{^{'}} + y = e^{t}, y (0) = 0, y^{^{'}} (0) = 9