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

Lösung

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

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e}{2} + \frac{- 2 x sin ( x ) - x cos ( x )}{5} + \frac{14}{25} sin (x) + \frac{2}{25} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e}{2} + \frac{- 2 x sin ( x ) - x cos ( x )}{5} + \frac{14}{25} sin (x) + \frac{2}{25} cos (x)

y = e^{- x} (c_{1} cos (x) + c_{2} sin (x)) + \frac{e}{2} + \frac{- 2 x sin ( x ) - x cos ( x )}{5} + \frac{14}{25} sin (x) + \frac{2}{25} cos (x)

y^{^{''}} - y^{^{'}} + 14 y = 4 + e^{\frac{x}{2}}

y^{^{''}} - 4 y = 32 t

y^{^{''}} - 5 y^{^{'}} + 6 y = - 12 + e^{t}

y^{^{'''}} + 2 y^{^{''}} - y^{^{'}} - 2 y = 5 - 4 x^{3}

y^{^{''}} - y = 7 t