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

Lösung

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

y = \frac{1}{e ^{2 x}} + \frac{c _{1}}{e ^{2 x} x}

Schritte zur Lösung

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

Solve linear ODE:

y = \frac{1}{e ^{2 x}} + \frac{c _{1}}{e ^{2 x} x}

y = \frac{1}{e ^{2 x}} + \frac{c _{1}}{e ^{2 x} x}

\int \frac{1}{5 x ^{2} + 20 x - 10} d x

x \to \frac{π}{3} lim (\frac{1}{sec ( x )})

\frac{d y}{cos ( x ) + y} = d x

\int_{0}^{1} sin^{2} (π x) d x

\frac{\partial}{\partial x} (arctan (x + 2 y))