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

Lösung

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

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{9}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{9}{4}

y = c_{1} e^{x} + c_{2} e^{- 2 x} - \frac{x ^{2}}{2} - \frac{x}{2} - \frac{9}{4}

y^{^{'''}} + y^{^{'}} = e^{x}, y (0) = 0

y^{^{''}} + 4 y^{^{'}} = sin^{2} (x)

d^{2} (d + 3)^{2} y = 9 e^{- 3 x}

y^{^{''}} - 11 y = e^{x}

y^{^{''}} + 256 y = 16 cos (3 t)