y^{''}-2y^'-3y=(12e^{4x})/(1+e^{2x)}

Lösung

y^{^{''}} - 2 y^{^{'}} - 3 y = \frac{12 e ^{4 x}}{1 + e ^{2 x}}

y = c_{1} e^{3 x} + c_{2} e^{- x} + 3 e^{3 x} arctan (e^{x}) + e^{- x} \cdot \int - \frac{3 e ^{5 x}}{1 + e ^{2 x}} d x

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) - 3 y = \frac{12 e ^{4 x}}{1 + e ^{2 x}}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} + 3 e^{3 x} arctan (e^{x}) + e^{- x} \cdot \int - \frac{3 e ^{5 x}}{1 + e ^{2 x}} d x

y = c_{1} e^{3 x} + c_{2} e^{- x} + 3 e^{3 x} arctan (e^{x}) + e^{- x} \cdot \int - \frac{3 e ^{5 x}}{1 + e ^{2 x}} d x

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

y^{^{''}} - 2 y^{^{'}} = 5 t^{4}, y (0) = 1, y^{^{'}} (0) = 0

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

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

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{- 4 x}