y^{''}-2y^'+y=(e^t)/((1+t^2))+3e^t

Lösung

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{( 1 + t ^{2} )} + 3 e^{t}

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{3}{2} e^{t} t^{2} + e^{t} t arctan (t) - \frac{3}{2} e^{t} - \frac{1}{2} e^{t} ln (t^{2} + 1)

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) + y = \frac{e ^{t}}{( 1 + t ^{2} )} + 3 e^{t}

Solve linear ODE:

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{3}{2} e^{t} t^{2} + e^{t} t arctan (t) - \frac{3}{2} e^{t} - \frac{1}{2} e^{t} ln (t^{2} + 1)

y = c_{1} e^{t} + c_{2} t e^{t} + \frac{3}{2} e^{t} t^{2} + e^{t} t arctan (t) - \frac{3}{2} e^{t} - \frac{1}{2} e^{t} ln (t^{2} + 1)

y^{^{''}} + 10 y^{^{'}} + 20 y = 2695 e^{2 t} cos (11 t)

(D^{2} + 4) y = cos (2 x)

y^{^{''}} + 2 y^{^{'}} + 5 y = 8 cos (x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 1 + x e^{x}

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