y^{''}+y^'-12y=4e^xsin(2x)+4e^{3x}+2

Lösung

y^{^{''}} + y^{^{'}} - 12 y = 4 e^{x} sin (2 x) + 4 e^{3 x} + 2

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{7}{29} e^{x} sin (2 x) - \frac{3}{29} e^{x} cos (2 x) + \frac{4 e ^{3 x} x}{7} - \frac{1}{6}

Schritte zur Lösung

y^{''} (x) + y^{'} (x) - 12 y = 4 e^{x} sin (2 x) + 4 e^{3 x} + 2

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{7}{29} e^{x} sin (2 x) - \frac{3}{29} e^{x} cos (2 x) + \frac{4 e ^{3 x} x}{7} - \frac{1}{6}

y = c_{1} e^{3 x} + c_{2} e^{- 4 x} - \frac{7}{29} e^{x} sin (2 x) - \frac{3}{29} e^{x} cos (2 x) + \frac{4 e ^{3 x} x}{7} - \frac{1}{6}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 2 y = 5 e^{3 x}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 15 y = (x + 1) e^{x}

2 y^{^{''}} + 3 y^{^{'}} - 2 y = x e^{- 2 x}

9 y^{^{''}} - 6 y^{^{'}} + y = 5 - x

y^{^{''}} + 3 y^{^{'}} + 2 y = sin (x), y (0) = 0, y^{^{'}} (0) = 2