y^'=sqrt(y^2-1)

Lösung

y^{^{'}} = y^{2} - 1

y = \frac{1}{2 e ^{t + c_{1}}} + \frac{e ^{t + c_{1}}}{2}

Schritte zur Lösung

y^{'} (t) = y^{2} - 1

Solve separable ODE:

y = \frac{1}{2 e ^{t + c_{1}}} + \frac{e ^{t + c_{1}}}{2}

y = \frac{1}{2 e ^{t + c_{1}}} + \frac{e ^{t + c_{1}}}{2}

\frac{d y}{d x} - 4 y = 0

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

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

y^{^{'}} = \frac{6 y x ^{2}}{x ^{3} + 1}

\frac{d y}{d x} = \frac{6 y}{x}, x > 0