y^{''}-3y^'-4y=xe^x+2cos(x)-sin(x)

Lösung

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

y = c_{1} e^{4 x} + c_{2} e^{- x} - \frac{e ^{x} x}{6} + \frac{1}{36} e^{x} - \frac{1}{34} sin (x) - \frac{13}{34} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- x} - \frac{e ^{x} x}{6} + \frac{1}{36} e^{x} - \frac{1}{34} sin (x) - \frac{13}{34} cos (x)

y = c_{1} e^{4 x} + c_{2} e^{- x} - \frac{e ^{x} x}{6} + \frac{1}{36} e^{x} - \frac{1}{34} sin (x) - \frac{13}{34} cos (x)

D (D - 1)^{3} y = (x^{2} + 2 x) e^{x}

y^{^{''}} + 4 y = \frac{cos ( 2 x )}{2}

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

y^{^{''}} - y = e^{- 2 t}

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