Internal problem ID [2330]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 37, page 171
Problem number: 17.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {-2 y y^{\prime }+{y^{\prime }}^{2} x=-4 x} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 30
dsolve(4*x-2*diff(y(x),x)*y(x)+diff(y(x),x)^2*x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -2 x \\ y \left (x \right ) &= 2 x \\ y \left (x \right ) &= \frac {4 c_{1}^{2}+x^{2}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.295 (sec). Leaf size: 43
DSolve[4*x-2*y'[x]*y[x]+y'[x]^2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x \cosh (-\log (x)+c_1) \\ y(x)\to -2 x \cosh (\log (x)+c_1) \\ y(x)\to -2 x \\ y(x)\to 2 x \\ \end{align*}