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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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

y^{^{''}} + 4 y = 5 e^{x} - 4 x^{2}

y^{^{''}} + x + y = 0

y^{^{''}} + y = 1, y (0) = 0, y (1) = 0

y^{^{''}} + 12 y^{^{'}} + 27 y = 64 e^{- 1 t}