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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

\frac{d h}{d t} = - \frac{3}{100} h - 15

x^{2} (H (x) x) (H (x) d x + x d H (x)) = 0

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

x y^{2} y^{^{'}} = x + 7

y^{^{'}} - x y = 5 x