490y^{''}+20y=8cos(6t)

Lösung

490 y^{^{''}} + 20 y = 8 cos (6 t)

y = c_{1} cos (\frac{2 t}{7}) + c_{2} sin (\frac{2 t}{7}) - \frac{2}{4405} cos (6 t)

Schritte zur Lösung

490 y^{''} (t) + 20 y = 8 cos (6 t)

Solve linear ODE:

y = c_{1} cos (\frac{2 t}{7}) + c_{2} sin (\frac{2 t}{7}) - \frac{2}{4405} cos (6 t)

y = c_{1} cos (\frac{2 t}{7}) + c_{2} sin (\frac{2 t}{7}) - \frac{2}{4405} cos (6 t)

\frac{d ^{2} y}{d x ^{2}} - 4 y = \frac{e ^{2 x}}{x}

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

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} = 4 + 6 sin (x)

y^{^{''}} + 6 y^{^{'}} + 9 y = - 4 x e^{- 2 x} + 2 e^{- 3 x} + 3

(d^{2} + 4 d + 5) y = 50 x + 13 e^{3 x}