y^{''}-2y^'+5y=exsin(x)

Lösung

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

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{e x sin ( x )}{5} + \frac{e x cos ( x )}{10} + \frac{7 e}{50} sin (x) + \frac{e}{50} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{e x sin ( x )}{5} + \frac{e x cos ( x )}{10} + \frac{7 e}{50} sin (x) + \frac{e}{50} cos (x)

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{e x sin ( x )}{5} + \frac{e x cos ( x )}{10} + \frac{7 e}{50} sin (x) + \frac{e}{50} cos (x)

x^{^{''}} - 5 x^{^{'}} + 6 x = 2 e^{t}

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

y^{^{''}} + 4 y^{^{'}} = 2 e^{- t}, y (0) = 2, y^{^{'}} (0) = 2

(D^{2} - 2 D + 1) y = 4 x^{2} e^{x}

x^{^{''}} + 4 x^{^{'}} + 3 x = 4 e^{- 2 t}, x (0) = 0, x^{^{'}} (0) = 0