(dy)/(dx)=(3x^2)/(e^y+1)

Lösung

\frac{d y}{d x} = \frac{3 x ^{2}}{e ^{y} + 1}

y = - W (\frac{1}{e ^{- c_{1} - x^{3}}}) + x^{3} + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = \frac{3 x ^{2}}{e ^{y} + 1}

Solve separable ODE:

y = - W (\frac{1}{e ^{- c_{1} - x^{3}}}) + x^{3} + c_{1}

y = - W (\frac{1}{e ^{- c_{1} - x^{3}}}) + x^{3} + c_{1}

y^{^{'}} = y^{2} t^{3}

\frac{d V}{d t} = 0.4 V

(3 x y^{2} + x^{3}) y^{^{'}} = 3 y^{3} + x^{2} y

(3 y^{2} x^{2} - 3 x^{2}) d x + (5 x^{3} y) d y = 0

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