(2y+yx^2)dy=(x+xy^2)dx

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

y^{^{'}} = 4 e^{3 x} e^{- 2 y}

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

\frac{( x ^{2} + 4 ) d y}{d x} + 3 x y = x

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

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