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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

(2 x + 1) d x + y^{2} d y = 0

y^{^{'}} + (cos (x)) y^{2} = 0

d x + sin (t) x d t sin (t) d t = 0

y^{^{'}} = \frac{5 + 12 x}{x y ^{2}}, y (1) = 3

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