y^{''}-y^'-2y=e^xcos(x)

Lösung

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

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{1}{10} e^{x} sin (x) - \frac{3}{10} e^{x} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{1}{10} e^{x} sin (x) - \frac{3}{10} e^{x} cos (x)

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{1}{10} e^{x} sin (x) - \frac{3}{10} e^{x} cos (x)

y^{^{''}} + 4 y = \frac{t}{2} - \frac{t cos ( 2 t )}{2}

y^{^{''}} - 7 y^{^{'}} - 8 y = 8 x^{2} - 2 x

y^{^{''}} + 16 y = cos (4 t), y (0) = 3, y^{^{'}} (0) = 2

3 \frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 25 y = cos (2 x)

(D^{2} + 4 D + 5) y = e^{(- x)} + 15 x