Internal problem ID [6877]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th
edition. 1997.
Section: CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number: 15.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x*diff(y(x),x)^2-(x^2+1)*diff(y(x),x)+x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \ln \left (x \right )+c_{1} y \left (x \right ) = \frac {x^{2}}{2}+c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[x*(y'[x])^2-(x^2+1)*y'[x]+x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{2}+c_1 y(x)\to \log (x)+c_1 \end{align*}