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#### karush

##### Well-known member

- Jan 31, 2012

- 2,928

$\textsf{Given: }$

$$\displaystyle y'=2xy^2, \quad y(0)=1$$

$\textit{Show that $y=\phi(x)=(1-x^2)^{-1}$ is a solution of the initial value problem}$

\begin{align*}\displaystyle

y'&=2xy^2\\

\frac{dy}{y^2}&=2x \\

y&=\color{red}{\frac{1}{(c_1-x^2)}}

\end{align*}

ok I went into confusion after 2x??

red is W|F