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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} - 15 y^{^{'}} + 54 y = e^{a x}

y^{^{'''}} + 9 y^{^{''}} + y^{^{'}} + 9 y = 16 e^{x} - 9

y^{^{''}} + 8 y^{^{'}} + 32 y = 2 e^{2 x}

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 4 e^{3} t ln (t)