(dy)/(dx)=sqrt(y^2-1)

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

x d x - 4 y d y = 0

sin (x) d x + \frac{1}{y} d y = 0

x d y + y d x = x^{4} y d y + x^{3} y^{2} d x

y^{^{'}} = \frac{y + x ^{2} y}{x}

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