y^{''}-5y=2x^3-4x^2-x+6

Lösung

y^{^{''}} - 5 y = 2 x^{3} - 4 x^{2} - x + 6

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{2 x ^{3}}{5} + \frac{4 x ^{2}}{5} - \frac{7 x}{25} - \frac{22}{25}

Schritte zur Lösung

y^{''} (x) - 5 y = 2 x^{3} - 4 x^{2} - x + 6

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{2 x ^{3}}{5} + \frac{4 x ^{2}}{5} - \frac{7 x}{25} - \frac{22}{25}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} - \frac{2 x ^{3}}{5} + \frac{4 x ^{2}}{5} - \frac{7 x}{25} - \frac{22}{25}

y^{^{''}} + 4 y^{^{'}} + 5 y = 10 e^{- 2 x} cos (x)

y^{^{''}} + 6 y^{^{'}} + 9 y = cos (x)

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

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 2 y = x e^{x}

(d^{2} - 1) y = x e^{x} sin (x)