y^{''}-3y^'+2y=(e^{2t})/(e^{2t)+1}

Lösung

y^{^{''}} - 3 y^{^{'}} + 2 y = \frac{e ^{2 t}}{e ^{2 t} + 1}

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

Schritte zur Lösung

y^{''} (t) - 3 y^{'} (t) + 2 y = \frac{e ^{2 t}}{e ^{2 t} + 1}

Solve linear ODE:

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

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

y^{^{''}} + 4 y = t^{2} + 8 e^{t}

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 (9 x - 2) e^{2 x}

y^{^{''}} + 25 y = 10 cos (5 x) + 15 sin (5 x)

y^{^{''}} - 7 y^{^{'}} + 12 y = x^{2} e^{x}

y^{^{''}} - y^{^{'}} - 20 y = 72 e^{2 t}