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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{'}} sin (x) + y cos (x) = 0, y (\frac{π}{4}) = 1

x \to 0 + lim ((\frac{1}{x})^{l n (x)})

d er i v a t i v e cos (ln (x))

\int_{0}^{1} \frac{e ^{- 2 x}}{2} d x

x \to 0 lim (sinh (x) cot (x))