3y^{''}-3y^'+y=-18+31x-11x^2+x^3

Lösung

3 y^{^{''}} - 3 y^{^{'}} + y = - 18 + 31 x - 11 x^{2} + x^{3}

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2 3}) + c_{2} sin (\frac{x}{2 3})) + x^{3} - 2 x^{2} + x - 3

Schritte zur Lösung

3 y^{''} (x) - 3 y^{'} (x) + y = - 18 + 31 x - 11 x^{2} + x^{3}

Solve linear ODE:

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2 3}) + c_{2} sin (\frac{x}{2 3})) + x^{3} - 2 x^{2} + x - 3

y = e^{\frac{x}{2}} (c_{1} cos (\frac{x}{2 3}) + c_{2} sin (\frac{x}{2 3})) + x^{3} - 2 x^{2} + x - 3

y^{^{''}} + \frac{2}{5} y^{^{'}} + \frac{1}{50} y = 100

y^{^{''}} - y^{^{'}} - 2 y = e^{- t}, y (0) = - 1, y^{^{'}} (0) = 2

2 y^{^{''}} + 9 y^{^{'}} - y = 22

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

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 2, y^{^{''}} (0) = - 1