(dy)/(dx)=(x+2)/(2y)

Lösung

\frac{d y}{d x} = \frac{x + 2}{2 y}

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

Schritte zur Lösung

\frac{d y}{d x} = \frac{x + 2}{2 y}

Solve separable ODE:

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

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

y^{^{'}} - 2 x y^{3} = 0, y (2) = 1

\frac{d x}{d t} = 3 - \frac{x}{100}

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

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

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