0.1y^{''}+50y^'+2000y=110cos(377x)

Lösung

0.1 y^{^{''}} + 50 y^{^{'}} + 2000 y = 110 cos (377 x)

y = c_{1} e^{50 (17 - 5) x} + c_{2} e^{- 50 (5 + 17) x} + 0.00411 \dots sin (377 x) - 0.00266 \dots cos (377 x)

Schritte zur Lösung

0.1 y^{''} (x) + 50 y^{'} (x) + 2000 y = 110 cos (377 x)

Solve linear ODE:

y = c_{1} e^{50 (17 - 5) x} + c_{2} e^{- 50 (5 + 17) x} + 0.00411 \dots sin (377 x) - 0.00266 \dots cos (377 x)

y = c_{1} e^{50 (17 - 5) x} + c_{2} e^{- 50 (5 + 17) x} + 0.00411 \dots sin (377 x) - 0.00266 \dots cos (377 x)

y^{^{''}} - 3 y^{^{'}} + 2 y = (x + 1)^{2}

(D^{2} - 4) y = cos^{2} (x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 8 e^{2 t} + 10 t^{2}

y^{^{''}} - 5 y^{^{'}} + 6 y = x

\frac{1}{6} y^{^{''}} + 6 y = 3 tan (6 t) - \frac{1}{3} e^{t}