y^'=a-y^2

Lösung

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

y = - \frac{a e ^{2 a t + 2 c_{1} a}}{1 - e ^{2 a (t + c_{1})}} - \frac{a}{1 - e ^{2 a (t + c_{1})}}

Schritte zur Lösung

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

Solve separable ODE:

y = - \frac{a e ^{2 a t + 2 c_{1} a}}{1 - e ^{2 a (t + c_{1})}} - \frac{a}{1 - e ^{2 a (t + c_{1})}}

y = - \frac{a e ^{2 a t + 2 c_{1} a}}{1 - e ^{2 a (t + c_{1})}} - \frac{a}{1 - e ^{2 a (t + c_{1})}}

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

x^{^{'}} + \frac{3}{200} x = 0.006

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

\frac{d p}{d t} = \frac{t \cdot cos ( t ^{2} )}{p ^{2}}

(y x^{2} - 4 y - x^{2} + 4) d x + d y = 0