(d^2y)/(dx^2)+2(dy)/(dx)+y=e^{-x}*ln(x)

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (1 + x y^{2})

h \to 0 lim (\frac{3}{h})

d er i v a t i v e 4 tan^{2} (7 x)

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

d er i v a t i v e f (x) = \frac{( x ^{2} - 1 )}{x ^{2} + 1}