y^{''}-4y^'-5y=2+e^{-t},y(0)=0,y^'(0)=0

Lösung

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 + e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

y = (- \frac{11}{36} + \frac{2}{5}) e^{5 t} + \frac{11}{36} e^{- t} - \frac{2}{5} - \frac{e ^{- t} t}{6}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) - 5 y = 2 + e^{- t}

Solve linear ODE:

y = (- \frac{11}{36} + \frac{2}{5}) e^{5 t} + \frac{11}{36} e^{- t} - \frac{2}{5} - \frac{e ^{- t} t}{6}

y = (- \frac{11}{36} + \frac{2}{5}) e^{5 t} + \frac{11}{36} e^{- t} - \frac{2}{5} - \frac{e ^{- t} t}{6}

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 t^{2} - 5

4 x^{^{''}} + x = t^{2} + 2 cos (3 t)

y^{^{''}} + 2 y^{^{'}} - 8 y = 2 e^{2 x}

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

3 y^{^{''}} + y^{^{'}} - 2 y = 2 cos (x)