y^{'''}-2y^{''}-4y^'+8y=e^{-3x}+8x^2

Lösung

y^{^{'''}} - 2 y^{^{''}} - 4 y^{^{'}} + 8 y = e^{- 3 x} + 8 x^{2}

y = c_{1} e^{- 2 x} + c_{2} e^{2 x} + c_{3} x e^{2 x} - \frac{1}{25} e^{- 3 x} + x^{2} + x + 1

Schritte zur Lösung

y^{'''} (x) - 2 y^{''} (x) - 4 y^{'} (x) + 8 y = e^{- 3 x} + 8 x^{2}

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} e^{2 x} + c_{3} x e^{2 x} - \frac{1}{25} e^{- 3 x} + x^{2} + x + 1

y = c_{1} e^{- 2 x} + c_{2} e^{2 x} + c_{3} x e^{2 x} - \frac{1}{25} e^{- 3 x} + x^{2} + x + 1

\frac{1}{6} y^{^{''}} + 6 y = tan (6 t) - \frac{1}{3} e^{3 t}

y^{^{''}} + 4 y^{^{'}} + 5 y = e^{- 2 x} sec (x)

y^{^{''}} - 5 y^{^{'}} + 4 y = 1

y^{^{''}} - 100 y = 9 t^{2} e^{10 t}

y^{^{''}} - 16 y = cosh (4 x)