Internal problem ID [6032]
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: 19.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y \left (y^{\prime }\right )^{2} x +\left (x +y\right ) y^{\prime }+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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 \relax (x ) = -\ln \relax (x )+c_{1} \\ y \relax (x ) = \sqrt {c_{1}-2 x} \\ y \relax (x ) = -\sqrt {c_{1}-2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.092 (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*}