Internal problem ID [2344]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 38, page 173
Problem number: 7.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {-2 y^{\prime } y+{y^{\prime }}^{2} x=-2 x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(2*x+diff(y(x),x)^2*x=2*diff(y(x),x)*y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {\left (-\frac {x^{2}}{c_{1}^{2}}-2\right ) c_{1}}{2} y \left (x \right ) = c_{1} x \end{align*}
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 63
DSolve[2*x+y'[x]*x==2*y'[x]*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{34} \left (\left (17+\sqrt {17}\right ) \log \left (\frac {4 y(x)}{x}+\sqrt {17}-1\right )-\left (\sqrt {17}-17\right ) \log \left (-\frac {4 y(x)}{x}+\sqrt {17}+1\right )\right )=-\log (x)+c_1,y(x)\right ] \]