y^{''}-3y=6x

Lösung

y^{^{''}} - 3 y = 6 x

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - 2 x

Schritte zur Lösung

y^{''} (x) - 3 y = 6 x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - 2 x

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - 2 x

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

\frac{1}{2} y^{^{''}} + 5 y^{^{'}} + 12 y = e^{- 4 x} (4 x - 2)

2 y^{^{''}} + 5 y^{^{'}} + 2 y = x^{3} + 9 e^{4 x}

y^{^{''}} + y = sin (t), y (0) = 9, y^{^{'}} (0) = 1

y^{^{''}} - 4 y^{^{'}} + 3 y = 2 t