4.9.2.1.8 Example 7 \(\left ( y^{\prime \prime }\right ) ^{2}-2y^{\prime \prime }+\left ( y^{\prime }\right ) ^{2}-2xy^{\prime }+x^{2}=0\)

\[ \left ( y^{\prime \prime }\right ) ^{2}-2y^{\prime \prime }+\left ( y^{\prime }\right ) ^{2}-2xy^{\prime }+x^{2}=0 \]

Since \(y\) is missing, then let \(y^{\prime }=u,y^{\prime \prime }=u^{\prime }\) and the ode becomes

\[ \left ( u^{\prime }\right ) ^{2}-2u^{\prime }+u^{2}-2xu+x^{2}=0 \]