y^'=x-xy-y+1

Lösung

y^{^{'}} = x - x y - y + 1

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

Schritte zur Lösung

y^{'} (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

y (y^{2} - 1)^{\frac{1}{2}} d x - (1 - x^{2})^{\frac{1}{2}} d y = 0

e^{x + y} \frac{d y}{d x} = x

y^{^{'}} = 6 x^{2} y

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

y^{^{'}} = 7 x^{2} y