y^{''}-3y^'+2y=(e^{2x})/(e^{2x)+1}

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = \frac{e ^{2 x}}{e ^{2 x} + 1}

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

Schritte zur Lösung

y^{''} (x) - 3 y^{'} (x) + 2 y = \frac{e ^{2 x}}{e ^{2 x} + 1}

Solve linear ODE:

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

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

so l v e f or D, D (t) = 5 cos (\frac{π}{6} t + \frac{7 π}{6}) + 3

y^{^{''}} - 10 y^{^{'}} + 25 y = e^{5 t} ln (t)

(D^{2} + 6 D + 9) y = \frac{16 e ^{- 3 x}}{x ^{2} + 1}

y^{^{''}} + 2 y^{^{'}} + 2 y = 5 sin (t) + 5 cos (t)

2 y^{^{''}} - 3 y^{^{'}} = 9 x^{2} + 10