(dy)/(dx)+y/(x(x-1))=(x-1)

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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

\int x^{\frac{1}{2}} ln (x) d x

\frac{d}{d x} (a + b x^{2})

x \to - 2 lim (g (x))

a re a y = e^{- 0.6 x}, y = 1.4 x + 1, x = 0, x = 5