Internal problem ID [8802]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 467.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y {y^{\prime }}^{2}-4 y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 92
dsolve(y(x)*diff(y(x),x)^2-4*x*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 y \left (x \right ) = \operatorname {RootOf}\left (-\ln \left (x \right )-\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2}+\sqrt {-\textit {\_a}^{2}+4}-2}{\textit {\_a} \left (\textit {\_a}^{2}-3\right )}d \textit {\_a} \right )+c_{1} \right ) x y \left (x \right ) = \operatorname {RootOf}\left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}-\frac {\textit {\_a}^{2}-\sqrt {-\textit {\_a}^{2}+4}-2}{\textit {\_a} \left (\textit {\_a}^{2}-3\right )}d \textit {\_a} +c_{1} \right ) x \end{align*}
✓ Solution by Mathematica
Time used: 60.178 (sec). Leaf size: 177
DSolve[y[x] - 4*x*y'[x] + y[x]*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \sqrt {\frac {8\ 2^{2/3} x^4+\sqrt [3]{2} \left (32 x^6-40 c_1{}^3 x^3+\sqrt {\left (c_1{}^4-16 c_1 x^3\right ){}^3}-c_1{}^6\right ){}^{2/3}+4 x^2 \sqrt [3]{32 x^6-40 c_1{}^3 x^3+\sqrt {\left (c_1{}^4-16 c_1 x^3\right ){}^3}-c_1{}^6}+4\ 2^{2/3} c_1{}^3 x}{\sqrt [3]{32 x^6-40 c_1{}^3 x^3+\sqrt {\left (c_1{}^4-16 c_1 x^3\right ){}^3}-c_1{}^6}}} \]