y^{''}+40y^'+6250y=100cos(10t)

Lösung

y^{^{''}} + 40 y^{^{'}} + 6250 y = 100 cos (10 t)

y = e^{- 20 t} (c_{1} cos (1526 t) + c_{2} sin (1526 t)) + \frac{16}{15193} sin (10 t) + \frac{246}{15193} cos (10 t)

Schritte zur Lösung

y^{''} (t) + 40 y^{'} (t) + 6250 y = 100 cos (10 t)

Solve linear ODE:

y = e^{- 20 t} (c_{1} cos (1526 t) + c_{2} sin (1526 t)) + \frac{16}{15193} sin (10 t) + \frac{246}{15193} cos (10 t)

y = e^{- 20 t} (c_{1} cos (1526 t) + c_{2} sin (1526 t)) + \frac{16}{15193} sin (10 t) + \frac{246}{15193} cos (10 t)

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

y^{^{''}} - y^{^{'}} + 14 y = 4 + e^{\frac{x}{2}}

y^{^{''}} - 4 y = 32 t

y^{^{''}} - 5 y^{^{'}} + 6 y = - 12 + e^{t}

y^{^{'''}} + 2 y^{^{''}} - y^{^{'}} - 2 y = 5 - 4 x^{3}