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]
\[ \boxed {-2 y^{\prime } y+{y^{\prime }}^{2} x=-4 x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
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 {\left (-\frac {x^{2}}{c_{1}^{2}}-4\right ) c_{1}}{2} \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*}