y^{''}+8y^'+12y=1-\H(t-3)

Lösung

y^{^{''}} + 8 y^{^{'}} + 12 y = 1 - H (t - 3)

y = c_{1} e^{- 2 t} + c_{2} e^{- 6 t} + e^{- 2 t} \cdot \int \frac{e ^{2 t} ( 1 - H ( t - 3 ) )}{4} d t + e^{- 6 t} \cdot \int - \frac{e ^{6 t} ( 1 - H ( t - 3 ) )}{4} d t

Schritte zur Lösung

y^{''} (t) + 8 y^{'} (t) + 12 y = 1 - H (t - 3)

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} e^{- 6 t} + e^{- 2 t} \cdot \int \frac{e ^{2 t} ( 1 - H ( t - 3 ) )}{4} d t + e^{- 6 t} \cdot \int - \frac{e ^{6 t} ( 1 - H ( t - 3 ) )}{4} d t

y = c_{1} e^{- 2 t} + c_{2} e^{- 6 t} + e^{- 2 t} \cdot \int \frac{e ^{2 t} ( 1 - H ( t - 3 ) )}{4} d t + e^{- 6 t} \cdot \int - \frac{e ^{6 t} ( 1 - H ( t - 3 ) )}{4} d t

y^{^{''}} - 6 y^{^{'}} + 9 y = 2, y^{^{'}} (0) = 6

y^{^{''}} - 2 y^{^{'}} - 15 y = - 37 t + 30 t^{2}

y^{^{''}} - y^{^{'}} - 6 y = 4 cos (3 x)

y^{^{'''}} + 3 y^{^{''}} - 4 y^{^{'}} - 12 y = 4 cos (x)

y^{^{'''}} - a y^{^{'}} = 1 + cosh (a x)