Internal problem ID [2346]
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: 9.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {4 {y^{\prime }}^{2} x +2 y^{\prime } x -y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 51
dsolve(4*diff(y(x),x)^2*x+2*diff(y(x),x)*x=y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {x}{4} y \left (x \right ) = \left (\frac {4 c_{1}}{x}+\frac {2 \sqrt {c_{1} x}}{x}\right ) x y \left (x \right ) = \left (\frac {4 c_{1}}{x}-\frac {2 \sqrt {c_{1} x}}{x}\right ) x \end{align*}
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 72
DSolve[4*y'[x]^2*x+2*y'[x]*x==y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{2 c_1} \left (-2 \sqrt {x}+e^{2 c_1}\right ) y(x)\to \frac {1}{4} e^{-4 c_1} \left (1+2 e^{2 c_1} \sqrt {x}\right ) y(x)\to 0 y(x)\to -\frac {x}{4} \end{align*}