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

Lösung

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

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{19 x}{2}) + c_{2} sin (\frac{19 x}{2})) + \frac{2 x}{5} - \frac{2}{25}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{19 x}{2}) + c_{2} sin (\frac{19 x}{2})) + \frac{2 x}{5} - \frac{2}{25}

y = e^{- \frac{x}{2}} (c_{1} cos (\frac{19 x}{2}) + c_{2} sin (\frac{19 x}{2})) + \frac{2 x}{5} - \frac{2}{25}

y^{^{''}} - 4 y^{^{'}} + 13 y = e^{2 t} \cdot sin (3 t), y (0) = 4

y^{^{''}} + y^{^{'}} = e^{x} + 3 x

l in e a r y^{^{''}} + 4 y = x^{2} + 5 cos (x)

y^{^{''}} - y^{^{'}} - 6 y = sin (x)

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