xy^'-y=y^2

Lösung

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

y = \frac{e ^{c_{1}} x}{1 - e ^{c_{1}} x}

Schritte zur Lösung

x y^{'} (x) - y = y^{2}

Solve separable ODE:

y = \frac{e ^{c_{1}} x}{1 - e ^{c_{1}} x}

y = \frac{e ^{c_{1}} x}{1 - e ^{c_{1}} x}

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

\frac{d y}{d x} - \frac{y}{x} = 0

(x + 1) y^{^{'}} + y^{2} = 0

\frac{d x}{d t} + \frac{x}{100} = 75

(x^{2} - 3) \frac{d y}{d x} = x (y^{2} + 16), y (2) = 4