y^{''}+4y^'+3y=8xe^x-6

Lösung

y^{^{''}} + 4 y^{^{'}} + 3 y = 8 x e^{x} - 6

y = c_{1} e^{- x} + c_{2} e^{- 3 x} + e^{x} x - \frac{3}{4} e^{x} - 2

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 3 y = 8 x e^{x} - 6

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 3 x} + e^{x} x - \frac{3}{4} e^{x} - 2

y = c_{1} e^{- x} + c_{2} e^{- 3 x} + e^{x} x - \frac{3}{4} e^{x} - 2

y^{^{''}} + 3 y^{^{'}} - 10 y = e^{- 5 x}

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

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

x^{^{''}} + x = tan (t)

y^{^{''}} + 3 y^{^{'}} + 4 y = 3 x + 2