\documentclass[a4paper,12pt]{article}
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\newcommand{\un}{\underline}
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\begin{document}

{\bf Question}

Use Lagrange's method to find the general solution of
$yuu_x+xuu_y=xy$.

\medskip

{\bf Answer}

Lagrange gives

$\ \ \ds\frac{dx}{d\xi}=yu,\ \ds\frac{dy}{d\xi}=xu,\
\ds\frac{du}{d\xi}=xy$

$\Rightarrow \ds\frac{dy}{dx}=\ds\frac{x}{y}$ and
$\ds\frac{du}{dy}=\ds\frac{y}{u}$

$\Rightarrow y^2-x^2=const$ and $u^2-y^2=const$

$\Rightarrow$ the general solution is:

$$u^2-y^2=f(x^2-y^2)$$

$$\Rightarrow \un{u^2=y^2+f(x^2-y^2)}$$

\end{document}