y^{''}-9y=(9x)/(e^{3x)}

Lösung

y^{^{''}} - 9 y = \frac{9 x}{e ^{3 x}}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{- e ^{- 3 x} x - 3 e ^{- 3 x} x ^{2}}{4} - \frac{e ^{- 3 x}}{24}

Schritte zur Lösung

y^{''} (x) - 9 y = \frac{9 x}{e ^{3 x}}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{- e ^{- 3 x} x - 3 e ^{- 3 x} x ^{2}}{4} - \frac{e ^{- 3 x}}{24}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{- e ^{- 3 x} x - 3 e ^{- 3 x} x ^{2}}{4} - \frac{e ^{- 3 x}}{24}

y^{^{''}} - y^{^{'}} - 2 y = sin (2 x)

y^{^{''}} - y^{^{'}} = e^{t} cos (t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 10 y^{^{'}} + 25 y = e^{5 x} ln (4 + x^{2})

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{x} - 9

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