y^{''}-4y^'+5=4sin(x)-25/8 x

Lösung

y^{^{''}} - 4 y^{^{'}} + 5 = 4 sin (x) - \frac{25}{8} x

y = c_{1} e^{4 x} + c_{2} - \frac{4}{17} sin (x) + \frac{16}{17} cos (x) + \frac{25 x ^{2}}{64} + \frac{185 x}{128}

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 5 = 4 sin (x) - \frac{25}{8} x

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} - \frac{4}{17} sin (x) + \frac{16}{17} cos (x) + \frac{25 x ^{2}}{64} + \frac{185 x}{128}

y = c_{1} e^{4 x} + c_{2} - \frac{4}{17} sin (x) + \frac{16}{17} cos (x) + \frac{25 x ^{2}}{64} + \frac{185 x}{128}

y^{^{'''}} - y^{^{'}} = 4 e^{- x} + 3 e^{x}

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{t} sin (t)

y^{^{''}} + 7 y + 12 y = t^{2} e^{- 3 t}

5 y^{^{''}} + 88 y^{^{'}} + 240 y = 82 sin (6 x)

(d^{2} - 4) y = e^{- 3 x} sin (e^{- x})