Internal problem ID [6019]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES
Page 309
Problem number: 7.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(x*diff(y(x),x)^2-(1+x*y(x))*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \ln \left (x \right )+c_{1} \\ y \left (x \right ) = {\mathrm e}^{x} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 20
DSolve[x*(y'[x])^2-(1+x*y[x])*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x \\ y(x)\to \log (x)+c_1 \\ \end{align*}