(dy)/(dx)=x(y^2-4)

Lösung

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

y = \frac{2 e ^{4 c_{1}}}{e ^{2 x^{2}} - e ^{4 c_{1}}} + \frac{2 e ^{2 x^{2}}}{e ^{2 x^{2}} - e ^{4 c_{1}}}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{2 e ^{4 c_{1}}}{e ^{2 x^{2}} - e ^{4 c_{1}}} + \frac{2 e ^{2 x^{2}}}{e ^{2 x^{2}} - e ^{4 c_{1}}}

y = \frac{2 e ^{4 c_{1}}}{e ^{2 x^{2}} - e ^{4 c_{1}}} + \frac{2 e ^{2 x^{2}}}{e ^{2 x^{2}} - e ^{4 c_{1}}}

\frac{d x}{d t} = x - a x

y = t^{2} ln (t^{2}) \frac{d y}{d t}

\frac{d x}{d t} = 4 x t

(\frac{y}{x})^{2} \frac{d y}{d x} = y^{3} - 1

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