y^{''}-2y^'+y=2000x^2-150e^x

Lösung

y^{^{''}} - 2 y^{^{'}} + y = 2000 x^{2} - 150 e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + 2000 x^{2} + 8000 x + 12000 - 75 x^{2} e^{x}

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + y = 2000 x^{2} - 150 e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + 2000 x^{2} + 8000 x + 12000 - 75 x^{2} e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + 2000 x^{2} + 8000 x + 12000 - 75 x^{2} e^{x}

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

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

y^{^{''}} + 7 y^{^{'}} + 14 y = 1096 \cdot e^{2 t} \cdot cos (8 t)

x^{^{''}} - 2 x^{^{'}} + x = 1 t^{2} e^{t}

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