y^{''}+y^'-6y=t-2pi,y(0)=1,y^'(0)=2

Lösung

y^{^{''}} + y^{^{'}} - 6 y = t - 2 π, y (0) = 1, y^{^{'}} (0) = 2

y = (1 + \frac{2 + 12 π}{90} - \frac{12 π - 1}{36}) e^{2 t} - \frac{2 + 12 π}{90} e^{- 3 t} - \frac{t}{6} + \frac{12 π - 1}{36}

Schritte zur Lösung

y^{''} (t) + y^{'} (t) - 6 y = t - 2 π

Solve linear ODE:

y = (1 + \frac{2 + 12 π}{90} - \frac{12 π - 1}{36}) e^{2 t} - \frac{2 + 12 π}{90} e^{- 3 t} - \frac{t}{6} + \frac{12 π - 1}{36}

y = (1 + \frac{2 + 12 π}{90} - \frac{12 π - 1}{36}) e^{2 t} - \frac{2 + 12 π}{90} e^{- 3 t} - \frac{t}{6} + \frac{12 π - 1}{36}

- v y^{^{''}} - a y = c

y^{^{''}} - 7 y^{^{'}} + 10 y = e^{3 x} (- 1 + 10 x)

y^{^{''}} - 9 y^{^{'}} + 18 y = e^{6 t}

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

y^{^{''}} + 4 y = - cos (3 t) - 2 sin (3 t)