2(d^2y)/(dx^2)+3(dy)/(dx)-2y=xe^{-2x}

Lösung

2 \frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 2 y = x e^{- 2 x}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - \frac{e ^{- 2 x} x ^{2}}{10} - \frac{2 e ^{- 2 x} x}{25}

Schritte zur Lösung

2 \frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 2 y = x e^{- 2 x}

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - \frac{e ^{- 2 x} x ^{2}}{10} - \frac{2 e ^{- 2 x} x}{25}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- 2 x} - \frac{e ^{- 2 x} x ^{2}}{10} - \frac{2 e ^{- 2 x} x}{25}

y^{^{''}} + 4 y^{^{'}} = x e^{4 x}

x^{^{''}} + 4 x^{^{'}} + 8 x = 4 e^{- 2 t} sin (2 t)

y^{^{''}} - 2 y^{^{'}} + 10 y = - sin (3 t)

y^{^{''''}} + y^{^{''}} = 7 x - 3 cos (x)

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