(d^2-1)y=e^x(1+x^2)

Lösung

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

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} - \frac{e ^{x} x ^{2}}{4} + \frac{3 e ^{x} x}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} - \frac{e ^{x} x ^{2}}{4} + \frac{3 e ^{x} x}{4}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} - \frac{e ^{x} x ^{2}}{4} + \frac{3 e ^{x} x}{4}

(d - 1)^{4} y = e^{x}

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

(d - 3)^{2} \cdot y = 2 e^{4 x}

(d^{2} - 4) \cdot y = x^{2}

y^{^{''}} + y^{^{'}} + 3 y = 9 x^{2} + 3