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

Lösung

y^{^{'}} = \frac{1}{2} (y^{2} - 1)

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

\frac{d x}{d t} = 60 - \frac{x}{100}

x y^{2} d x + x^{2} y d y = 0

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

y^{^{'}} - x y = 0

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