Internal problem ID [2315]
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: 2.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x y {y^{\prime }}^{2}+\left (y+x \right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(x*y(x)*diff(y(x),x)^2+(x+y(x))*diff(y(x),x)+1=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\ln \left (x \right )+c_{1} y \left (x \right ) = \sqrt {-2 x +c_{1}} y \left (x \right ) = -\sqrt {-2 x +c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 53
DSolve[x*y[x]*y'[x]^2+(x+y[x])*y'[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} \sqrt {-x+c_1} y(x)\to \sqrt {2} \sqrt {-x+c_1} y(x)\to -\log (x)+c_1 \end{align*}