(1-y^2)dx=-(xy-y)dy

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

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

y^{^{'}} = - \frac{1}{y}

[1 + t^{2}] \frac{d y}{d t} = 1 + y^{2}

y^{^{'}} = x^{2} y, y (0) = 1

y^{3} y^{^{'}} + 4 x y^{4} = 8 x