y^{''}-7y^'-18y=-x+cos(3x)

Lösung

y^{^{''}} - 7 y^{^{'}} - 18 y = - x + cos (3 x)

y = c_{1} e^{9 x} + c_{2} e^{- 2 x} + \frac{x}{18} - \frac{7}{324} - \frac{7}{390} sin (3 x) - \frac{3}{130} cos (3 x)

Schritte zur Lösung

y^{''} (x) - 7 y^{'} (x) - 18 y = - x + cos (3 x)

Solve linear ODE:

y = c_{1} e^{9 x} + c_{2} e^{- 2 x} + \frac{x}{18} - \frac{7}{324} - \frac{7}{390} sin (3 x) - \frac{3}{130} cos (3 x)

y = c_{1} e^{9 x} + c_{2} e^{- 2 x} + \frac{x}{18} - \frac{7}{324} - \frac{7}{390} sin (3 x) - \frac{3}{130} cos (3 x)

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

y^{^{''}} - y = \frac{1}{cosh ( x )}

x^{^{''}} + 2 x^{^{'}} + x = e^{- 2 t}, x (0) = 2

y^{^{''}} + 4 y^{^{'}} + 13 y = cos (3 x)

4 y^{^{''}} - y = sin (x)