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

Lösung

y^{^{''}} - 2 y^{^{'}} + y = \frac{2 e ^{x}}{x ^{2} - 1}

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

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + y = \frac{2 e ^{x}}{x ^{2} - 1}

Solve linear ODE:

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

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

y^{^{''}} + 5 y^{^{'}} + 6 y = - 19 t e^{(2 t)}

y^{^{''}} + 9 y = g (t), y (0) = 4, y^{^{'}} (0) = 0

y^{^{''}} + 5 y^{^{'}} + 4 y = 2 e^{- 5 x}, y (0) = 4, y^{^{'}} (0) = 3

D^{2} (D + 2) y = 2 + e^{\frac{- t}{2}}

x^{^{''}} + x^{^{'}} = 2 t + 1