(xy-y)y^'=x^2y-y+x^2-1

Lösung

(x y - y) y^{^{'}} = x^{2} y - y + x^{2} - 1

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

Schritte zur Lösung

(x y - y) y^{'} (x) = x^{2} y - y + x^{2} - 1

Solve separable ODE:

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

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

y^{^{'}} + y^{5} = 0

x^{2} y^{^{'}} + 2 x y = 0

y^{^{'}} = - 3 x y

y = \frac{1}{2 y ^{^{'}} ( x ) ^{2}}

x^{^{'}} - 2 x = 0