y^{''}-y^'-2y=cosh^2(t)

Lösung

y^{^{''}} - y^{^{'}} - 2 y = cosh^{2} (t)

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{12} e^{2 t} (- \frac{1}{4} e^{- 4 t} - e^{- 2 t} + t) + e^{- t} \cdot \int - \frac{e ^{t} cosh ^{2} ( t )}{3} d t

Schritte zur Lösung

y^{''} (t) - y^{'} (t) - 2 y = cosh^{2} (t)

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{12} e^{2 t} (- \frac{1}{4} e^{- 4 t} - e^{- 2 t} + t) + e^{- t} \cdot \int - \frac{e ^{t} cosh ^{2} ( t )}{3} d t

y = c_{1} e^{2 t} + c_{2} e^{- t} + \frac{1}{12} e^{2 t} (- \frac{1}{4} e^{- 4 t} - e^{- 2 t} + t) + e^{- t} \cdot \int - \frac{e ^{t} cosh ^{2} ( t )}{3} d t

y^{^{''}} - y = e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 y = e^{2 x} \frac{1}{x}

y^{^{''}} - 3 y^{^{'}} + y = 2 e^{3 t}, y (0) = 0, y^{^{'}} (0) = 4

y^{^{''}} + 3 y^{^{'}} + 2 y = 6 e^{2 t}

y^{^{'''}} + 2 y^{^{''}} - 11 y^{^{'}} - 12 y = 4