(dy)/(dx)=(y(-2x+4))/((x^2+1)(x-1)^2)

Lösung

\frac{d y}{d x} = \frac{y ( - 2 x + 4 )}{( x ^{2} + 1 ) ( x - 1 ) ^{2}}

y = \frac{e ^{\frac{x a r c t a n ( x ) - a r c t a n ( x ) - 1 + c _{1} x - c _{1}}{x - 1}} x ^{2} + e ^{\frac{x a r c t a n ( x ) - a r c t a n ( x ) - 1 + c _{1} x - c _{1}}{x - 1}}}{x ^{2} - 2 x + 1}

Schritte zur Lösung

\frac{d y}{d x} = \frac{y ( - 2 x + 4 )}{( x ^{2} + 1 ) ( x - 1 ) ^{2}}

Solve separable ODE:

y = \frac{e ^{\frac{x a r c t a n ( x ) - a r c t a n ( x ) - 1 + c _{1} x - c _{1}}{x - 1}} x ^{2} + e ^{\frac{x a r c t a n ( x ) - a r c t a n ( x ) - 1 + c _{1} x - c _{1}}{x - 1}}}{x ^{2} - 2 x + 1}

y = \frac{e ^{\frac{x a r c t a n ( x ) - a r c t a n ( x ) - 1 + c _{1} x - c _{1}}{x - 1}} x ^{2} + e ^{\frac{x a r c t a n ( x ) - a r c t a n ( x ) - 1 + c _{1} x - c _{1}}{x - 1}}}{x ^{2} - 2 x + 1}