x(dy)/(dx)=(1+y)^2

Lösung

x \frac{d y}{d x} = (1 + y)^{2}

y = - \frac{1}{ln ( x ) + c _{1}} - \frac{ln ( x )}{ln ( x ) + c _{1}} - \frac{c _{1}}{ln ( x ) + c _{1}}

Schritte zur Lösung

x \frac{d y}{d x} = (1 + y)^{2}

Solve separable ODE:

y = - \frac{1}{ln ( x ) + c _{1}} - \frac{ln ( x )}{ln ( x ) + c _{1}} - \frac{c _{1}}{ln ( x ) + c _{1}}

y = - \frac{1}{ln ( x ) + c _{1}} - \frac{ln ( x )}{ln ( x ) + c _{1}} - \frac{c _{1}}{ln ( x ) + c _{1}}

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

y^{^{'}} = - 1 - 2 y

\frac{d y}{d x} = 7 y^{2} x^{3}

3 y^{2} \frac{d y}{d x} = 2 x

\frac{d y}{d x} = \frac{x ^{2} + x + 1}{y + 1}