y^{''}+y^'-6y=30-30\H(t-4)

Lösung

y^{^{''}} + y^{^{'}} - 6 y = 30 - 30 H (t - 4)

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

Schritte zur Lösung

y^{''} (t) + y^{'} (t) - 6 y = 30 - 30 H (t - 4)

Solve linear ODE:

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

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

y^{^{''}} + 10 y^{^{'}} + 16 y = 3 cos (5 t) + 4 sin (5 t)

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

y^{^{''}} + 4 y^{^{'}} + 5 y = 35 e^{- 4 x}, y (0) = - 2

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{- x} sin (x) + x e^{3 x}

y^{^{''}} - 2 y^{^{'}} = 1, y (0) = 2, y^{^{'}} (0) = 1