y^{'''}-y=x^3-1

Lösung

y^{^{'''}} - y = x^{3} - 1

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

8 y^{^{''}} + y = t, y (0) = 0, y^{^{'}} (0) = 0

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

y^{^{''}} + y^{^{'}} + \frac{256}{3} x = 50 cos (3 x)

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

y^{^{''}} + 2 y^{^{'}} = e^{t}