y^{''}+y^'-12y=e^x+e^{2x}-1

Lösung

y^{^{''}} + y^{^{'}} - 12 y = e^{x} + e^{2 x} - 1

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{1}{10} e^{x} - \frac{1}{6} e^{2 x} + \frac{1}{12}

Schritte zur Lösung

y^{''} (x) + y^{'} (x) - 12 y = e^{x} + e^{2 x} - 1

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{1}{10} e^{x} - \frac{1}{6} e^{2 x} + \frac{1}{12}

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{1}{10} e^{x} - \frac{1}{6} e^{2 x} + \frac{1}{12}

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

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

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

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 x^{2} + 12

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