- #1
karush
Gold Member
MHB
- 3,269
- 5
$\tiny{2.3.2}$
1000
$\textsf{Given: }$
$$\displaystyle y'=2xy^2, \quad y(0)=1$$
$\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
1000
$\textsf{Given: }$
$$\displaystyle y'=2xy^2, \quad y(0)=1$$
$\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
Last edited: