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

Lösung

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

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + (e - \frac{4 e}{5}) x sin (x) + \frac{2 e x cos ( x )}{5} + (2 e - \frac{48 e}{25}) sin (x) + \frac{14 e}{25} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + (e - \frac{4 e}{5}) x sin (x) + \frac{2 e x cos ( x )}{5} + (2 e - \frac{48 e}{25}) sin (x) + \frac{14 e}{25} cos (x)

y = e^{x} (c_{1} cos (x) + c_{2} sin (x)) + (e - \frac{4 e}{5}) x sin (x) + \frac{2 e x cos ( x )}{5} + (2 e - \frac{48 e}{25}) sin (x) + \frac{14 e}{25} cos (x)

y^{^{''}} + 6 y^{^{'}} + 5 y = e^{x}

y^{^{''}} + 5 y^{^{'}} + 6 = sin (x) - cos (2 x)

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

y^{^{'''}} - 6 y^{^{''}} + 25 y^{^{'}} = 68 e^{2 x}

(d - 3)^{3} y = e^{3 x}