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

Lösung

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

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{- e ^{- 2 x} x ^{2} + e ^{x} x ^{2}}{6} + \frac{- e ^{- 2 x} x - e ^{x} x}{9}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{- e ^{- 2 x} x ^{2} + e ^{x} x ^{2}}{6} + \frac{- e ^{- 2 x} x - e ^{x} x}{9}

y = c_{1} e^{x} + c_{2} e^{- 2 x} + \frac{- e ^{- 2 x} x ^{2} + e ^{x} x ^{2}}{6} + \frac{- e ^{- 2 x} x - e ^{x} x}{9}

\frac{1}{4} y^{^{''}} + 4 y = 2 tan (4 t) - \frac{1}{3} e^{2 t}

y^{^{''}} + 5 y^{^{'}} + 4 y = 1 + x + x^{2}

y^{^{''}} + y = - x^{2}, y (0) = 0, y (1) = 1

y^{^{''}} + y^{^{'}} - 2 y = u π (t) - u^{2} π (t)

y^{^{''}} + 4 y^{^{'}} + 3 y = - 19 t e^{3 t}