y^{''}-8y^'+12y=e^{2x}(x^2-1)

Lösung

y^{^{''}} - 8 y^{^{'}} + 12 y = e^{2 x} (x^{2} - 1)

y = c_{1} e^{6 x} + c_{2} e^{2 x} - \frac{e ^{2 x} x ^{3}}{12} - \frac{e ^{2 x} x ^{2}}{16} + \frac{7 e ^{2 x} x}{32}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 12 y = e^{2 x} (x^{2} - 1)

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} e^{2 x} - \frac{e ^{2 x} x ^{3}}{12} - \frac{e ^{2 x} x ^{2}}{16} + \frac{7 e ^{2 x} x}{32}

y = c_{1} e^{6 x} + c_{2} e^{2 x} - \frac{e ^{2 x} x ^{3}}{12} - \frac{e ^{2 x} x ^{2}}{16} + \frac{7 e ^{2 x} x}{32}

y^{^{''}} + y^{^{'}} - 12 y = 2 t e - 4 t, y (0) = - 5, y^{^{'}} (0) = - 4

y^{^{''}} + 25 y = 5 tan^{2} (5 x) cos (5 x)

y^{^{''}} + y = 2 sin (2 t)

y^{^{'''}} - 2 y^{^{''}} - 4 y^{^{'}} + 8 = 0

y^{^{''}} - 8 y^{^{'}} - 9 y = 2 e^{- x} - 9 x