y^{''}-2y^'+5y=4e^xsin(2x)+5x

Lösung

y^{^{''}} - 2 y^{^{'}} + 5 y = 4 e^{x} sin (2 x) + 5 x

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

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 5 y = 4 e^{x} sin (2 x) + 5 x

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + 5 y = 4 e^{- t} \cdot cos (2 t)

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 5 t

\frac{d ^{2} y}{d x ^{2}} (1) + \frac{d y}{d x} (10) + 9 y = 18

y^{^{''}} + 2 y^{^{'}} + 4 y = t cos (t)

y^{^{''}} - 2 y^{^{'}} - 3 y = 2 sin (x)