y^'+y^2=3

Lösung

y^{^{'}} + y^{2} = 3

y = - \frac{3 e ^{23 t + 23 c_{1}}}{1 - e ^{23 (t + c_{1})}} - \frac{3}{1 - e ^{23 (t + c_{1})}}

Schritte zur Lösung

y^{'} (t) + y^{2} = 3

Solve separable ODE:

y = - \frac{3 e ^{23 t + 23 c_{1}}}{1 - e ^{23 (t + c_{1})}} - \frac{3}{1 - e ^{23 (t + c_{1})}}

y = - \frac{3 e ^{23 t + 23 c_{1}}}{1 - e ^{23 (t + c_{1})}} - \frac{3}{1 - e ^{23 (t + c_{1})}}

\frac{d y}{d x} = \frac{x ^{2}}{y}, y (0) = 2

y^{^{'}} = \frac{x y ^{2}}{8} + y^{2}

\frac{d y}{d x} = x^{2} (y - 6), y (0) = 8

\frac{d y}{d x} - 2 cos (x) y = 0

y^{\frac{1}{2}} y^{^{'}} = 1 - y^{\frac{3}{2}}