(dy}{dx}=\frac{x^2e^{x^3-y^2})/y

Lösung

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

y = ln (\frac{2}{3} e^{x^{3}} + c_{1}), y = - ln (\frac{2}{3} e^{x^{3}} + c_{1})

Schritte zur Lösung

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

Solve separable ODE:

y = ln (\frac{2}{3} e^{x^{3}} + c_{1}), y = - ln (\frac{2}{3} e^{x^{3}} + c_{1})

y = ln (\frac{2}{3} e^{x^{3}} + c_{1}), y = - ln (\frac{2}{3} e^{x^{3}} + c_{1})

\frac{d y}{d x} - x^{3} = x^{3} y

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

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

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

\frac{d y}{d x} + 5 x y = 8 x, y (0) = 4