2y^{''}+20y^'+50y=10sin(3x)

Lösung

2 y^{^{''}} + 20 y^{^{'}} + 50 y = 10 sin (3 x)

y = c_{1} e^{- 5 x} + c_{2} x e^{- 5 x} + \frac{20}{289} sin (3 x) - \frac{75}{578} cos (3 x)

Schritte zur Lösung

2 y^{''} (x) + 20 y^{'} (x) + 50 y = 10 sin (3 x)

Solve linear ODE:

y = c_{1} e^{- 5 x} + c_{2} x e^{- 5 x} + \frac{20}{289} sin (3 x) - \frac{75}{578} cos (3 x)

y = c_{1} e^{- 5 x} + c_{2} x e^{- 5 x} + \frac{20}{289} sin (3 x) - \frac{75}{578} cos (3 x)

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

y^{^{'''}} - 19 y^{^{'}} + 30 y = x^{2} \cdot e^{2 x}

y^{^{''}} - 4 y^{^{'}} - 5 y = 125, y (0) = 0, y^{^{'}} (0) = 0

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

y^{^{''}} - y = \frac{1}{e ^{x} + 1}