y^{''}-2y^'+9y=2cos(x)

Lösung

y^{^{''}} - 2 y^{^{'}} + 9 y = 2 cos (x)

y = e^{x} (c_{1} cos (2^{1 + \frac{1}{2}} x) + c_{2} sin (2^{1 + \frac{1}{2}} x)) - \frac{1}{17} sin (x) + \frac{4}{17} cos (x)

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 9 y = 2 cos (x)

Solve linear ODE:

y = e^{x} (c_{1} cos (2^{1 + \frac{1}{2}} x) + c_{2} sin (2^{1 + \frac{1}{2}} x)) - \frac{1}{17} sin (x) + \frac{4}{17} cos (x)

y = e^{x} (c_{1} cos (2^{1 + \frac{1}{2}} x) + c_{2} sin (2^{1 + \frac{1}{2}} x)) - \frac{1}{17} sin (x) + \frac{4}{17} cos (x)

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

\frac{d ^{2} x}{d t ^{2}} + 4 \frac{d x}{d t} + 4 x = 4 e^{- 2 t}

(D^{2} + D) y = sin (x)

y^{^{''}} + 10 y^{^{'}} + 24 y = e^{x} + 3 x

y^{^{''}} + k^{2} y = sin (b x)